---
_id: '14934'
abstract:
- lang: eng
text: "We study random perturbations of a Riemannian manifold (M, g) by means of
so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the
given manifold. The fields\r\nh• : ω \x02→ hω will act on the manifold via the
conformal transformation g \x02→ gω := e2hω g.\r\nOur focus will be on the regular
case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated
Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric
and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion,
spectral bound, or spectral gap change under the influence of the noise. And if
so, is\r\nit possible to quantify these dependencies in terms of key parameters
of the noise? Another\r\ngoal is to define and analyze in detail the Fractional
Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent
interest."
acknowledgement: "The authors would like to thank Matthias Erbar and Ronan Herry for
valuable discussions on this project. They are also grateful to Nathanaël Berestycki,
and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24],
and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous
version of the proof of Proposition 3.10. The authors feel very much indebted to
an anonymous reviewer for his/her careful reading and the many valuable suggestions
that have significantly contributed to the improvement of the paper. L.D.S. gratefully
acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC
1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65
at Institute of Science and Technology Austria. This research was funded in whole
or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open
access, the authors have applied a CC BY public copyright licence to any Author
Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully
acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff
Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Karl Theodor
full_name: Sturm, Karl Theodor
last_name: Sturm
citation:
ama: Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian
geometry. Potential Analysis. 2024. doi:10.1007/s11118-023-10118-0
apa: Dello Schiavo, L., Kopfer, E., & Sturm, K. T. (2024). A discovery tour
in random Riemannian geometry. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-023-10118-0
chicago: Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery
Tour in Random Riemannian Geometry.” Potential Analysis. Springer Nature,
2024. https://doi.org/10.1007/s11118-023-10118-0.
ieee: L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random
Riemannian geometry,” Potential Analysis. Springer Nature, 2024.
ista: Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian
geometry. Potential Analysis.
mla: Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.”
Potential Analysis, Springer Nature, 2024, doi:10.1007/s11118-023-10118-0.
short: L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis (2024).
date_created: 2024-02-04T23:00:54Z
date_published: 2024-01-26T00:00:00Z
date_updated: 2024-02-05T13:04:23Z
day: '26'
department:
- _id: JaMa
doi: 10.1007/s11118-023-10118-0
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s11118-023-10118-0
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Potential Analysis
publication_identifier:
eissn:
- 1572-929X
issn:
- 0926-2601
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A discovery tour in random Riemannian geometry
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '14732'
abstract:
- lang: eng
text: 'Fragmented landscapes pose a significant threat to the persistence of species
as they are highly susceptible to heightened risk of extinction due to the combined
effects of genetic and demographic factors such as genetic drift and demographic
stochasticity. This paper explores the intricate interplay between genetic load
and extinction risk within metapopulations with a focus on understanding the impact
of eco-evolutionary feedback mechanisms. We distinguish between two models of
selection: soft selection, characterised by subpopulations maintaining carrying
capacity despite load, and hard selection, where load can significantly affect
population size. Within the soft selection framework, we investigate the impact
of gene flow on genetic load at a single locus, while also considering the effect
of selection strength and dominance coefficient. We subsequently build on this
to examine how gene flow influences both population size and load under hard selection
as well as identify critical thresholds for metapopulation persistence. Our analysis
employs the diffusion, semi-deterministic and effective migration approximations.
Our findings reveal that under soft selection, even modest levels of migration
can significantly alleviate the burden of load. In sharp contrast, with hard selection,
a much higher degree of gene flow is required to mitigate load and prevent the
collapse of the metapopulation. Overall, this study sheds light into the crucial
role migration plays in shaping the dynamics of genetic load and extinction risk
in fragmented landscapes, offering valuable insights for conservation strategies
and the preservation of diversity in a changing world.'
article_processing_charge: No
author:
- first_name: Oluwafunmilola O
full_name: Olusanya, Oluwafunmilola O
id: 41AD96DC-F248-11E8-B48F-1D18A9856A87
last_name: Olusanya
orcid: 0000-0003-1971-8314
- first_name: Kseniia
full_name: Khudiakova, Kseniia
id: 4E6DC800-AE37-11E9-AC72-31CAE5697425
last_name: Khudiakova
orcid: 0000-0002-6246-1465
- first_name: Himani
full_name: Sachdeva, Himani
id: 42377A0A-F248-11E8-B48F-1D18A9856A87
last_name: Sachdeva
citation:
ama: Olusanya OO, Khudiakova K, Sachdeva H. Genetic load, eco-evolutionary feedback
and extinction in a metapopulation. bioRxiv. doi:10.1101/2023.12.02.569702
apa: Olusanya, O. O., Khudiakova, K., & Sachdeva, H. (n.d.). Genetic load, eco-evolutionary
feedback and extinction in a metapopulation. bioRxiv. https://doi.org/10.1101/2023.12.02.569702
chicago: Olusanya, Oluwafunmilola O, Kseniia Khudiakova, and Himani Sachdeva. “Genetic
Load, Eco-Evolutionary Feedback and Extinction in a Metapopulation.” BioRxiv,
n.d. https://doi.org/10.1101/2023.12.02.569702.
ieee: O. O. Olusanya, K. Khudiakova, and H. Sachdeva, “Genetic load, eco-evolutionary
feedback and extinction in a metapopulation,” bioRxiv. .
ista: Olusanya OO, Khudiakova K, Sachdeva H. Genetic load, eco-evolutionary feedback
and extinction in a metapopulation. bioRxiv, 10.1101/2023.12.02.569702.
mla: Olusanya, Oluwafunmilola O., et al. “Genetic Load, Eco-Evolutionary Feedback
and Extinction in a Metapopulation.” BioRxiv, doi:10.1101/2023.12.02.569702.
short: O.O. Olusanya, K. Khudiakova, H. Sachdeva, BioRxiv (n.d.).
date_created: 2024-01-04T09:35:54Z
date_published: 2023-12-04T00:00:00Z
date_updated: 2025-05-26T09:05:10Z
day: '04'
department:
- _id: NiBa
- _id: JaMa
doi: 10.1101/2023.12.02.569702
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.biorxiv.org/content/10.1101/2023.12.02.569702v1
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: c08d3278-5a5b-11eb-8a69-fdb09b55f4b8
grant_number: P32896
name: Causes and consequences of population fragmentation
- _id: 34d33d68-11ca-11ed-8bc3-ec13763c0ca8
grant_number: '26293'
name: The impact of deleterious mutations on small populations
- _id: 34c872fe-11ca-11ed-8bc3-8534b82131e6
grant_number: '26380'
name: Polygenic Adaptation in a Metapopulation
publication: bioRxiv
publication_status: submitted
related_material:
record:
- id: '14711'
relation: dissertation_contains
status: public
status: public
title: Genetic load, eco-evolutionary feedback and extinction in a metapopulation
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2023'
...
---
_id: '13145'
abstract:
- lang: eng
text: We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary
finite diffuse measure space. We provide an interpretation of this characterization
in analogy with the Mecke identity for Poisson point processes.
acknowledgement: Research supported by the Sfb 1060 The Mathematics of Emergent Effects
(University of Bonn). L.D.S. gratefully acknowledges funding of his current position
by the Austrian Science Fund (FWF) through project ESPRIT 208.
article_processing_charge: No
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Eugene
full_name: Lytvynov, Eugene
last_name: Lytvynov
citation:
ama: Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson
measure. Electronic Communications in Probability. 2023;28:1-12. doi:10.1214/23-ECP528
apa: Dello Schiavo, L., & Lytvynov, E. (2023). A Mecke-type characterization
of the Dirichlet–Ferguson measure. Electronic Communications in Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP528
chicago: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization
of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability.
Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP528.
ieee: L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson
measure,” Electronic Communications in Probability, vol. 28. Institute
of Mathematical Statistics, pp. 1–12, 2023.
ista: Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson
measure. Electronic Communications in Probability. 28, 1–12.
mla: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization
of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability,
vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:10.1214/23-ECP528.
short: L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28
(2023) 1–12.
date_created: 2023-06-18T22:00:48Z
date_published: 2023-05-05T00:00:00Z
date_updated: 2023-12-13T11:24:57Z
day: '05'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/23-ECP528
external_id:
isi:
- '001042025400001'
file:
- access_level: open_access
checksum: 4a543fe4b3f9e747cc52167c17bfb524
content_type: application/pdf
creator: dernst
date_created: 2023-06-19T09:37:40Z
date_updated: 2023-06-19T09:37:40Z
file_id: '13152'
file_name: 2023_ElectronCommProbability_Schiavo.pdf
file_size: 271434
relation: main_file
success: 1
file_date_updated: 2023-06-19T09:37:40Z
has_accepted_license: '1'
intvolume: ' 28'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1-12
project:
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
publication: Electronic Communications in Probability
publication_identifier:
eissn:
- 1083-589X
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: A Mecke-type characterization of the Dirichlet–Ferguson measure
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2023'
...
---
_id: '13177'
abstract:
- lang: eng
text: In this note we study the eigenvalue growth of infinite graphs with discrete
spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type
inequalities and that the total measure is finite. In this sense, the associated
operators on these graphs display similarities to elliptic operators on bounded
domains in the continuum. Specifically, we prove lower bounds on the eigenvalue
growth and show by examples that corresponding upper bounds cannot be established.
acknowledgement: The second author was supported by the priority program SPP2026 of
the German Research Foundation (DFG). The fourth author was supported by the German
Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the
German Research Foundation (DFG) via RTG 1523/2.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Bobo
full_name: Hua, Bobo
last_name: Hua
- first_name: Matthias
full_name: Keller, Matthias
last_name: Keller
- first_name: Michael
full_name: Schwarz, Michael
last_name: Schwarz
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue
growth on graphs with finite measure. Proceedings of the American Mathematical
Society. 2023;151(8):3401-3414. doi:10.1090/proc/14361
apa: Hua, B., Keller, M., Schwarz, M., & Wirth, M. (2023). Sobolev-type inequalities
and eigenvalue growth on graphs with finite measure. Proceedings of the American
Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/14361
chicago: Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type
Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings
of the American Mathematical Society. American Mathematical Society, 2023.
https://doi.org/10.1090/proc/14361.
ieee: B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and
eigenvalue growth on graphs with finite measure,” Proceedings of the American
Mathematical Society, vol. 151, no. 8. American Mathematical Society, pp.
3401–3414, 2023.
ista: Hua B, Keller M, Schwarz M, Wirth M. 2023. Sobolev-type inequalities and eigenvalue
growth on graphs with finite measure. Proceedings of the American Mathematical
Society. 151(8), 3401–3414.
mla: Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs
with Finite Measure.” Proceedings of the American Mathematical Society,
vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:10.1090/proc/14361.
short: B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical
Society 151 (2023) 3401–3414.
date_created: 2023-07-02T22:00:43Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2023-11-14T13:07:09Z
day: '01'
department:
- _id: JaMa
doi: 10.1090/proc/14361
external_id:
arxiv:
- '1804.08353'
isi:
- '000988204400001'
intvolume: ' 151'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1804.08353'
month: '08'
oa: 1
oa_version: Preprint
page: 3401-3414
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sobolev-type inequalities and eigenvalue growth on graphs with finite measure
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 151
year: '2023'
...
---
_id: '13271'
abstract:
- lang: eng
text: "In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s,\r\nfor
parameters (p, q, s) that are best possible, where B and C are any n-by-n positive-definite
matrices, and A is any n-by-n matrix. We also obtain the monotonicity versions
of trace functionals of this type. As applications, we extend some results in
Carlen et al. (Linear Algebra Appl 490:174–185, 2016), Hiai and Petz (Publ Res
Inst Math Sci 48(3):525-542, 2012) and resolve a conjecture in Al-Rashed and Zegarliński
(Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) in the matrix
setting. Other conjectures in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum
Probab Relat Top 17(4):1450029, 2014) will also be discussed. We also show that
some related trace functionals are not concave in general. Such concavity results
were expected to hold in different problems."
acknowledgement: I am grateful to Boguslaw Zegarliński for asking me the questions
in [3] and for helpful communication. I also want to thank Paata Ivanisvili for
drawing [25] to my attention and for useful correspondence. Many thanks to the anonymous
referee for the valuable comments and for pointing out some errors in an earlier
version of the paper. This work is partially supported by the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement
No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Zhang H. Some convexity and monotonicity results of trace functionals. Annales
Henri Poincare. 2023. doi:10.1007/s00023-023-01345-7
apa: Zhang, H. (2023). Some convexity and monotonicity results of trace functionals.
Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-023-01345-7
chicago: Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.”
Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-023-01345-7.
ieee: H. Zhang, “Some convexity and monotonicity results of trace functionals,”
Annales Henri Poincare. Springer Nature, 2023.
ista: Zhang H. 2023. Some convexity and monotonicity results of trace functionals.
Annales Henri Poincare.
mla: Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.”
Annales Henri Poincare, Springer Nature, 2023, doi:10.1007/s00023-023-01345-7.
short: H. Zhang, Annales Henri Poincare (2023).
date_created: 2023-07-23T22:01:15Z
date_published: 2023-07-08T00:00:00Z
date_updated: 2023-12-13T11:33:46Z
day: '08'
department:
- _id: JaMa
doi: 10.1007/s00023-023-01345-7
ec_funded: 1
external_id:
arxiv:
- '2108.05785'
isi:
- '001025709100001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2108.05785
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Some convexity and monotonicity results of trace functionals
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '13318'
abstract:
- lang: eng
text: Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free
constants that grow subexponentially in the degree (Defant et al. in Math Ann
374(1):653–680, 2019). Such inequalities have found great applications in learning
low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th
annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated
by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality
for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand,
KKL and Friedgut’s theorems and the learnability of quantum Boolean functions,
2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et
al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894).
In this paper, we give a new proof of these Bohnenblust–Hille inequalities for
qubit system with constants that are dimension-free and of exponential growth
in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials.
Using similar ideas, we also study learning problems of low degree quantum observables
and Bohr’s radius phenomenon on quantum Boolean cubes.
acknowledgement: The research of A.V. is supported by NSF DMS-1900286, DMS-2154402
and by Hausdorff Center for Mathematics. H.Z. is supported by the Lise Meitner fellowship,
Austrian Science Fund (FWF) M3337. This work is partially supported by NSF DMS-1929284
while both authors were in residence at the Institute for Computational and Experimental
Research in Mathematics in Providence, RI, during the Harmonic Analysis and Convexity
program.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Alexander
full_name: Volberg, Alexander
last_name: Volberg
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Volberg A, Zhang H. Noncommutative Bohnenblust–Hille inequalities. Mathematische
Annalen. 2023. doi:10.1007/s00208-023-02680-0
apa: Volberg, A., & Zhang, H. (2023). Noncommutative Bohnenblust–Hille inequalities.
Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-023-02680-0
chicago: Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille
Inequalities.” Mathematische Annalen. Springer Nature, 2023. https://doi.org/10.1007/s00208-023-02680-0.
ieee: A. Volberg and H. Zhang, “Noncommutative Bohnenblust–Hille inequalities,”
Mathematische Annalen. Springer Nature, 2023.
ista: Volberg A, Zhang H. 2023. Noncommutative Bohnenblust–Hille inequalities. Mathematische
Annalen.
mla: Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.”
Mathematische Annalen, Springer Nature, 2023, doi:10.1007/s00208-023-02680-0.
short: A. Volberg, H. Zhang, Mathematische Annalen (2023).
date_created: 2023-07-30T22:01:03Z
date_published: 2023-07-24T00:00:00Z
date_updated: 2023-12-13T11:36:20Z
day: '24'
department:
- _id: JaMa
doi: 10.1007/s00208-023-02680-0
external_id:
arxiv:
- '2210.14468'
isi:
- '001035665500001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00208-023-02680-0
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
publication: Mathematische Annalen
publication_identifier:
eissn:
- 1432-1807
issn:
- 0025-5831
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Noncommutative Bohnenblust–Hille inequalities
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '13319'
abstract:
- lang: eng
text: We prove that the generator of the L2 implementation of a KMS-symmetric quantum
Markov semigroup can be expressed as the square of a derivation with values in
a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially
symmetric semigroups and the second-named author for GNS-symmetric semigroups.
This result hinges on the introduction of a new completely positive map on the
algebra of bounded operators on the GNS Hilbert space. This transformation maps
symmetric Markov operators to symmetric Markov operators and is essential to obtain
the required inner product on the Hilbert bimodule.
acknowledgement: The authors are grateful to Martijn Caspers for helpful comments
on a preliminary version of this manuscript. M. V. was supported by the NWO Vidi
grant VI.Vidi.192.018 ‘Non-commutative harmonic analysis and rigidity of operator
algebras’. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit
Programme [ESP 156]. For the purpose of Open Access, the authors have applied a
CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising
from this submission. Open access funding provided by Austrian Science Fund (FWF).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Matthijs
full_name: Vernooij, Matthijs
last_name: Vernooij
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups.
Communications in Mathematical Physics. 2023;403:381-416. doi:10.1007/s00220-023-04795-6
apa: Vernooij, M., & Wirth, M. (2023). Derivations and KMS-symmetric quantum
Markov semigroups. Communications in Mathematical Physics. Springer Nature.
https://doi.org/10.1007/s00220-023-04795-6
chicago: Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric
Quantum Markov Semigroups.” Communications in Mathematical Physics. Springer
Nature, 2023. https://doi.org/10.1007/s00220-023-04795-6.
ieee: M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,”
Communications in Mathematical Physics, vol. 403. Springer Nature, pp.
381–416, 2023.
ista: Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups.
Communications in Mathematical Physics. 403, 381–416.
mla: Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum
Markov Semigroups.” Communications in Mathematical Physics, vol. 403, Springer
Nature, 2023, pp. 381–416, doi:10.1007/s00220-023-04795-6.
short: M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023)
381–416.
date_created: 2023-07-30T22:01:03Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2024-01-30T12:16:32Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00220-023-04795-6
external_id:
arxiv:
- '2303.15949'
isi:
- '001033655400002'
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page: 381-416
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grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
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issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivations and KMS-symmetric quantum Markov semigroups
tmp:
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 403
year: '2023'
...
---
_id: '10145'
abstract:
- lang: eng
text: We study direct integrals of quadratic and Dirichlet forms. We show that each
quasi-regular Dirichlet space over a probability space admits a unique representation
as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same
underlying topology. The same holds for each quasi-regular strongly local Dirichlet
space over a metrizable Luzin σ-finite Radon measure space, and admitting carré
du champ operator. In this case, the representation is only projectively unique.
acknowledgement: The author is grateful to Professors Sergio Albeverio and Andreas
Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the
present work, and for respectively pointing out the references [1, 13], and [3,
20]. Finally, he is especially grateful to an anonymous Reviewer for their very
careful reading and their suggestions which improved the readability of the paper.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals
and applications. Potential Analysis. 2023;58:573-615. doi:10.1007/s11118-021-09951-y
apa: Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct
integrals and applications. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-021-09951-y
chicago: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct
Integrals and Applications.” Potential Analysis. Springer Nature, 2023.
https://doi.org/10.1007/s11118-021-09951-y.
ieee: L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals
and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615,
2023.
ista: Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct
integrals and applications. Potential Analysis. 58, 573–615.
mla: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct
Integrals and Applications.” Potential Analysis, vol. 58, Springer Nature,
2023, pp. 573–615, doi:10.1007/s11118-021-09951-y.
short: L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.
date_created: 2021-10-17T22:01:17Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2023-10-04T09:19:12Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s11118-021-09951-y
ec_funded: 1
external_id:
arxiv:
- '2003.01366'
isi:
- '000704213400001'
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language:
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month: '03'
oa: 1
oa_version: Published Version
page: 573-615
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Potential Analysis
publication_identifier:
eissn:
- 1572-929X
issn:
- 0926-2601
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ergodic decomposition of Dirichlet forms via direct integrals and applications
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2023'
...
---
_id: '12087'
abstract:
- lang: eng
text: Following up on the recent work on lower Ricci curvature bounds for quantum
systems, we introduce two noncommutative versions of curvature-dimension bounds
for symmetric quantum Markov semigroups over matrix algebras. Under suitable such
curvature-dimension conditions, we prove a family of dimension-dependent functional
inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power
in the noncommutative setting. We also provide examples satisfying certain curvature-dimension
conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers
over group algebras and generalized depolarizing semigroups.
acknowledgement: H.Z. is supported by the European Union’s Horizon 2020 research and
innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411
and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges
support from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (Grant Agreement No. 716117) and from the
Austrian Science Fund (FWF) through grant number F65. Both authors would like to
thank Jan Maas for fruitful discussions and helpful comments. Open access funding
provided by Austrian Science Fund (FWF).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov
semigroups. Annales Henri Poincare. 2023;24:717-750. doi:10.1007/s00023-022-01220-x
apa: Wirth, M., & Zhang, H. (2023). Curvature-dimension conditions for symmetric
quantum Markov semigroups. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01220-x
chicago: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for
Symmetric Quantum Markov Semigroups.” Annales Henri Poincare. Springer
Nature, 2023. https://doi.org/10.1007/s00023-022-01220-x.
ieee: M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum
Markov semigroups,” Annales Henri Poincare, vol. 24. Springer Nature, pp.
717–750, 2023.
ista: Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum
Markov semigroups. Annales Henri Poincare. 24, 717–750.
mla: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric
Quantum Markov Semigroups.” Annales Henri Poincare, vol. 24, Springer Nature,
2023, pp. 717–50, doi:10.1007/s00023-022-01220-x.
short: M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.
date_created: 2022-09-11T22:01:57Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2023-08-14T11:39:28Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00023-022-01220-x
ec_funded: 1
external_id:
arxiv:
- '2105.08303'
isi:
- '000837499800002'
file:
- access_level: open_access
checksum: 8c7b185eba5ccd92ef55c120f654222c
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date_created: 2023-08-14T11:38:28Z
date_updated: 2023-08-14T11:38:28Z
file_id: '14051'
file_name: 2023_AnnalesHenriPoincare_Wirth.pdf
file_size: 554871
relation: main_file
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file_date_updated: 2023-08-14T11:38:28Z
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isi: 1
language:
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month: '03'
oa: 1
oa_version: Published Version
page: 717-750
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Curvature-dimension conditions for symmetric quantum Markov semigroups
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...
---
_id: '12104'
abstract:
- lang: eng
text: We study ergodic decompositions of Dirichlet spaces under intertwining via
unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular
Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore,
every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces
is decomposable over their ergodic decompositions up to conjugation via an isomorphism
of the corresponding indexing spaces.
acknowledgement: Research supported by the Austrian Science Fund (FWF) grant F65 at
the Institute of Science and Technology Austria and by the European Research Council
(ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully
acknowledges funding of his current position by the Austrian Science Fund (FWF)
through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding
of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme
(Grant No. 156).
article_number: '9'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order
isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7
apa: Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet
forms under order isomorphisms. Journal of Evolution Equations. Springer
Nature. https://doi.org/10.1007/s00028-022-00859-7
chicago: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of
Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations.
Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7.
ieee: L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms
under order isomorphisms,” Journal of Evolution Equations, vol. 23, no.
1. Springer Nature, 2023.
ista: Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms
under order isomorphisms. Journal of Evolution Equations. 23(1), 9.
mla: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet
Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23,
no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7.
short: L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).
date_created: 2023-01-08T23:00:53Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2023-06-28T11:54:35Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00028-022-00859-7
ec_funded: 1
external_id:
isi:
- '000906214600004'
file:
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checksum: 1f34f3e2cb521033de6154f274ea3a4e
content_type: application/pdf
creator: dernst
date_created: 2023-01-20T10:45:06Z
date_updated: 2023-01-20T10:45:06Z
file_id: '12325'
file_name: 2023_JourEvolutionEquations_DelloSchiavo.pdf
file_size: 422612
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has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Journal of Evolution Equations
publication_identifier:
eissn:
- 1424-3202
issn:
- 1424-3199
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ergodic decompositions of Dirichlet forms under order isomorphisms
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 23
year: '2023'
...
---
_id: '12911'
abstract:
- lang: eng
text: 'This paper establishes new connections between many-body quantum systems,
One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport
(OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional
composite quantum system at positive temperature as a non-commutative entropy
regularized Optimal Transport problem. We develop a new approach to fully characterize
the dual-primal solutions in such non-commutative setting. The mathematical formalism
is particularly relevant in quantum chemistry: numerical realizations of the many-electron
ground-state energy can be computed via a non-commutative version of Sinkhorn
algorithm. Our approach allows to prove convergence and robustness of this algorithm,
which, to our best knowledge, were unknown even in the two marginal case. Our
methods are based on a priori estimates in the dual problem, which we believe
to be of independent interest. Finally, the above results are extended in 1RDMFT
setting, where bosonic or fermionic symmetry conditions are enforced on the problem.'
acknowledgement: "This work started when A.G. was visiting the Erwin Schrödinger Institute
and then continued when D.F. and L.P visited the Theoretical Chemistry Department
of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places
and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature
suggestions in the early state of the project. The authors also thank J. Maas and
R. Seiringer for their feedback and useful comments to a first draft of the article.
Finally, we acknowledge the high quality review done by the anonymous referee of
our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F
acknowledges support by the European Research Council (ERC) under the European Union's
Horizon 2020 research and innovation programme (grant agreements No 716117 and No
694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council
under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of
his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences
and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges
support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the
Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813."
article_number: '109963'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
- first_name: Augusto
full_name: Gerolin, Augusto
last_name: Gerolin
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal
transport approach to quantum composite systems at positive temperature. Journal
of Functional Analysis. 2023;285(4). doi:10.1016/j.jfa.2023.109963
apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (2023). A non-commutative
entropic optimal transport approach to quantum composite systems at positive temperature.
Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.109963
chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative
Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.”
Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963.
ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic
optimal transport approach to quantum composite systems at positive temperature,”
Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023.
ista: Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal
transport approach to quantum composite systems at positive temperature. Journal
of Functional Analysis. 285(4), 109963.
mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach
to Quantum Composite Systems at Positive Temperature.” Journal of Functional
Analysis, vol. 285, no. 4, 109963, Elsevier, 2023, doi:10.1016/j.jfa.2023.109963.
short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis
285 (2023).
date_created: 2023-05-07T22:01:02Z
date_published: 2023-08-15T00:00:00Z
date_updated: 2023-11-14T13:21:01Z
day: '15'
department:
- _id: RoSe
- _id: JaMa
doi: 10.1016/j.jfa.2023.109963
ec_funded: 1
external_id:
arxiv:
- '2106.11217'
isi:
- '000990804300001'
intvolume: ' 285'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2106.11217
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: ' F06504'
name: Taming Complexity in Partial Di erential Systems
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
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relation: earlier_version
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scopus_import: '1'
status: public
title: A non-commutative entropic optimal transport approach to quantum composite
systems at positive temperature
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 285
year: '2023'
...
---
_id: '12959'
abstract:
- lang: eng
text: "This paper deals with the large-scale behaviour of dynamical optimal transport
on Zd\r\n-periodic graphs with general lower semicontinuous and convex energy
densities. Our main contribution is a homogenisation result that describes the
effective behaviour of the discrete problems in terms of a continuous optimal
transport problem. The effective energy density can be explicitly expressed in
terms of a cell formula, which is a finite-dimensional convex programming problem
that depends non-trivially on the local geometry of the discrete graph and the
discrete energy density. Our homogenisation result is derived from a Γ\r\n-convergence
result for action functionals on curves of measures, which we prove under very
mild growth conditions on the energy density. We investigate the cell formula
in several cases of interest, including finite-volume discretisations of the Wasserstein
distance, where non-trivial limiting behaviour occurs."
acknowledgement: J.M. gratefully acknowledges support by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No. 716117). J.M and L.P. also acknowledge support from the Austrian
Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support
by the German Research Foundation through the Hausdorff Center for Mathematics and
the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation)—350398276. We thank the
anonymous reviewer for the careful reading and for useful suggestions. Open access
funding provided by Austrian Science Fund (FWF).
article_number: '143'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Peter
full_name: Gladbach, Peter
last_name: Gladbach
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of dynamical optimal
transport on periodic graphs. Calculus of Variations and Partial Differential
Equations. 2023;62(5). doi:10.1007/s00526-023-02472-z
apa: Gladbach, P., Kopfer, E., Maas, J., & Portinale, L. (2023). Homogenisation
of dynamical optimal transport on periodic graphs. Calculus of Variations and
Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-023-02472-z
chicago: Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation
of Dynamical Optimal Transport on Periodic Graphs.” Calculus of Variations
and Partial Differential Equations. Springer Nature, 2023. https://doi.org/10.1007/s00526-023-02472-z.
ieee: P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical
optimal transport on periodic graphs,” Calculus of Variations and Partial Differential
Equations, vol. 62, no. 5. Springer Nature, 2023.
ista: Gladbach P, Kopfer E, Maas J, Portinale L. 2023. Homogenisation of dynamical
optimal transport on periodic graphs. Calculus of Variations and Partial Differential
Equations. 62(5), 143.
mla: Gladbach, Peter, et al. “Homogenisation of Dynamical Optimal Transport on Periodic
Graphs.” Calculus of Variations and Partial Differential Equations, vol.
62, no. 5, 143, Springer Nature, 2023, doi:10.1007/s00526-023-02472-z.
short: P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and
Partial Differential Equations 62 (2023).
date_created: 2023-05-14T22:01:00Z
date_published: 2023-04-28T00:00:00Z
date_updated: 2023-10-04T11:34:49Z
day: '28'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00526-023-02472-z
ec_funded: 1
external_id:
arxiv:
- '2110.15321'
isi:
- '000980588900001'
file:
- access_level: open_access
checksum: 359bee38d94b7e0aa73925063cb8884d
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T11:34:10Z
date_updated: 2023-10-04T11:34:10Z
file_id: '14393'
file_name: 2023_CalculusEquations_Gladbach.pdf
file_size: 1240995
relation: main_file
success: 1
file_date_updated: 2023-10-04T11:34:10Z
has_accepted_license: '1'
intvolume: ' 62'
isi: 1
issue: '5'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
name: Dissipation and Dispersion in Nonlinear Partial Differential Equations
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
eissn:
- 1432-0835
issn:
- 0944-2669
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Homogenisation of dynamical optimal transport on periodic graphs
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 62
year: '2023'
...
---
_id: '10797'
abstract:
- lang: eng
text: We consider symmetric partial exclusion and inclusion processes in a general
graph in contact with reservoirs, where we allow both for edge disorder and well-chosen
site disorder. We extend the classical dualities to this context and then we derive
new orthogonal polynomial dualities. From the classical dualities, we derive the
uniqueness of the non-equilibrium steady state and obtain correlation inequalities.
Starting from the orthogonal polynomial dualities, we show universal properties
of n-point correlation functions in the non-equilibrium steady state for systems
with at most two different reservoir parameters, such as a chain with reservoirs
at left and right ends.
- lang: fre
text: Nous considérons des processus d’exclusion partielle, et des processus d’inclusion
sur un graphe général en contact avec des réservoirs. Nous autorisons la présence
de inhomogenéités sur les arrêts ainsi que sur les sommets du graph. Nous généralisons
les “dualités classiques” dans ce contexte et nous démontrons des nouvelles dualités
orthogonales. À partir des dualités classiques, nous démontrons l’unicité de l’état
stationnaire non-équilibre, ainsi que des inégalités de corrélation. À partir
des dualités orthogonales nous démontrons des propriétés universelles des fonctions
de corrélation à n points dans l’état stationnaire non-équilibre pour des systèmes
avec deux paramètres de réservoirs inégaux, comme par exemple une chaîne avec
des réservoirs à droite et à gauche.
acknowledgement: The authors would like to thank Gioia Carinci and Cristian Giardinà
for useful discussions. F.R. and S.F. thank Jean-René Chazottes for a stay at CPHT
(Institut Polytechnique de Paris), in the realm of Chaire d’Alembert (Paris-Saclay
University), where part of this work was performed. S.F. acknowledges Simona Villa
for her support in creating the picture. S.F. acknowledges financial support from
NWO via the grant TOP1.17.019. F.S. acknowledges financial support from the European
Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie
grant agreement No. 754411.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Simone
full_name: Floreani, Simone
last_name: Floreani
- first_name: Frank
full_name: Redig, Frank
last_name: Redig
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: Floreani S, Redig F, Sau F. Orthogonal polynomial duality of boundary driven
particle systems and non-equilibrium correlations. Annales de l’institut Henri
Poincare (B) Probability and Statistics. 2022;58(1):220-247. doi:10.1214/21-AIHP1163
apa: Floreani, S., Redig, F., & Sau, F. (2022). Orthogonal polynomial duality
of boundary driven particle systems and non-equilibrium correlations. Annales
de l’institut Henri Poincare (B) Probability and Statistics. Institute of
Mathematical Statistics. https://doi.org/10.1214/21-AIHP1163
chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Orthogonal Polynomial
Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.”
Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute
of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AIHP1163.
ieee: S. Floreani, F. Redig, and F. Sau, “Orthogonal polynomial duality of boundary
driven particle systems and non-equilibrium correlations,” Annales de l’institut
Henri Poincare (B) Probability and Statistics, vol. 58, no. 1. Institute of
Mathematical Statistics, pp. 220–247, 2022.
ista: Floreani S, Redig F, Sau F. 2022. Orthogonal polynomial duality of boundary
driven particle systems and non-equilibrium correlations. Annales de l’institut
Henri Poincare (B) Probability and Statistics. 58(1), 220–247.
mla: Floreani, Simone, et al. “Orthogonal Polynomial Duality of Boundary Driven
Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri
Poincare (B) Probability and Statistics, vol. 58, no. 1, Institute of Mathematical
Statistics, 2022, pp. 220–47, doi:10.1214/21-AIHP1163.
short: S. Floreani, F. Redig, F. Sau, Annales de l’institut Henri Poincare (B) Probability
and Statistics 58 (2022) 220–247.
date_created: 2022-02-27T23:01:50Z
date_published: 2022-02-01T00:00:00Z
date_updated: 2023-10-17T12:49:43Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/21-AIHP1163
ec_funded: 1
external_id:
arxiv:
- '2007.08272'
isi:
- '000752489300010'
intvolume: ' 58'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2007.08272
month: '02'
oa: 1
oa_version: Preprint
page: 220-247
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium
correlations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2022'
...
---
_id: '11330'
abstract:
- lang: eng
text: In this article we study the noncommutative transport distance introduced
by Carlen and Maas and its entropic regularization defined by Becker and Li. We
prove a duality formula that can be understood as a quantum version of the dual
Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions
of a Hamilton–Jacobi–Bellmann equation.
acknowledgement: "The author wants to thank Jan Maas for helpful comments. He also
acknowledges financial support from the Austrian Science Fund (FWF) through Grant
Number F65 and from the European Research Council (ERC) under the European Union’s
Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria)."
article_number: '19'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Wirth M. A dual formula for the noncommutative transport distance. Journal
of Statistical Physics. 2022;187(2). doi:10.1007/s10955-022-02911-9
apa: Wirth, M. (2022). A dual formula for the noncommutative transport distance.
Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02911-9
chicago: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.”
Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02911-9.
ieee: M. Wirth, “A dual formula for the noncommutative transport distance,” Journal
of Statistical Physics, vol. 187, no. 2. Springer Nature, 2022.
ista: Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal
of Statistical Physics. 187(2), 19.
mla: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.”
Journal of Statistical Physics, vol. 187, no. 2, 19, Springer Nature, 2022,
doi:10.1007/s10955-022-02911-9.
short: M. Wirth, Journal of Statistical Physics 187 (2022).
date_created: 2022-04-24T22:01:43Z
date_published: 2022-04-08T00:00:00Z
date_updated: 2023-08-03T06:37:49Z
day: '08'
ddc:
- '510'
- '530'
department:
- _id: JaMa
doi: 10.1007/s10955-022-02911-9
ec_funded: 1
external_id:
isi:
- '000780305000001'
file:
- access_level: open_access
checksum: f3e0b00884b7dde31347a3756788b473
content_type: application/pdf
creator: dernst
date_created: 2022-04-29T11:24:23Z
date_updated: 2022-04-29T11:24:23Z
file_id: '11338'
file_name: 2022_JourStatisticalPhysics_Wirth.pdf
file_size: 362119
relation: main_file
success: 1
file_date_updated: 2022-04-29T11:24:23Z
has_accepted_license: '1'
intvolume: ' 187'
isi: 1
issue: '2'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- '15729613'
issn:
- '00224715'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A dual formula for the noncommutative transport distance
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 187
year: '2022'
...
---
_id: '11354'
abstract:
- lang: eng
text: We construct a recurrent diffusion process with values in the space of probability
measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process
is associated with the Dirichlet form defined by integration of the Wasserstein
gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional
base spaces to the modified massive Arratia flow over the unit interval described
in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800).
Together with two different constructions of the process, we discuss its ergodicity,
invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.
acknowledgement: Research supported by the Sonderforschungsbereich 1060 and the Hausdorff
Center for Mathematics. The author gratefully acknowledges funding of his current
position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the
European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr.
Jan Maas).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold. Annals of Probability. 2022;50(2):591-648.
doi:10.1214/21-AOP1541
apa: Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of
probability measures over a closed Riemannian manifold. Annals of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1541
chicago: Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space
of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability.
Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1541.
ieee: L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold,” Annals of Probability, vol.
50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.
ista: Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.
mla: Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability
Measures over a Closed Riemannian Manifold.” Annals of Probability, vol.
50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:10.1214/21-AOP1541.
short: L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.
date_created: 2022-05-08T22:01:44Z
date_published: 2022-03-01T00:00:00Z
date_updated: 2023-10-17T12:50:24Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/21-AOP1541
ec_funded: 1
external_id:
arxiv:
- '1811.11598'
isi:
- '000773518500005'
intvolume: ' 50'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1811.11598'
month: '03'
oa: 1
oa_version: Preprint
page: 591-648
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Annals of Probability
publication_identifier:
eissn:
- 2168-894X
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Dirichlet–Ferguson diffusion on the space of probability measures over
a closed Riemannian manifold
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2022'
...
---
_id: '11447'
abstract:
- lang: eng
text: Empirical essays of fitness landscapes suggest that they may be rugged, that
is having multiple fitness peaks. Such fitness landscapes, those that have multiple
peaks, necessarily have special local structures, called reciprocal sign epistasis
(Poelwijk et al. in J Theor Biol 272:141–144, 2011). Here, we investigate the
quantitative relationship between the number of fitness peaks and the number of
reciprocal sign epistatic interactions. Previously, it has been shown (Poelwijk
et al. in J Theor Biol 272:141–144, 2011) that pairwise reciprocal sign epistasis
is a necessary but not sufficient condition for the existence of multiple peaks.
Applying discrete Morse theory, which to our knowledge has never been used in
this context, we extend this result by giving the minimal number of reciprocal
sign epistatic interactions required to create a given number of peaks.
acknowledgement: We are grateful to Herbert Edelsbrunner and Jeferson Zapata for helpful
discussions. Open access funding provided by Austrian Science Fund (FWF). Partially
supported by the ERC Consolidator (771209–CharFL) and the FWF Austrian Science Fund
(I5127-B) grants to FAK.
article_number: '74'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Raimundo J
full_name: Saona Urmeneta, Raimundo J
id: BD1DF4C4-D767-11E9-B658-BC13E6697425
last_name: Saona Urmeneta
orcid: 0000-0001-5103-038X
- first_name: Fyodor
full_name: Kondrashov, Fyodor
id: 44FDEF62-F248-11E8-B48F-1D18A9856A87
last_name: Kondrashov
orcid: 0000-0001-8243-4694
- first_name: Kseniia
full_name: Khudiakova, Kseniia
id: 4E6DC800-AE37-11E9-AC72-31CAE5697425
last_name: Khudiakova
orcid: 0000-0002-6246-1465
citation:
ama: Saona Urmeneta RJ, Kondrashov F, Khudiakova K. Relation between the number
of peaks and the number of reciprocal sign epistatic interactions. Bulletin
of Mathematical Biology. 2022;84(8). doi:10.1007/s11538-022-01029-z
apa: Saona Urmeneta, R. J., Kondrashov, F., & Khudiakova, K. (2022). Relation
between the number of peaks and the number of reciprocal sign epistatic interactions.
Bulletin of Mathematical Biology. Springer Nature. https://doi.org/10.1007/s11538-022-01029-z
chicago: Saona Urmeneta, Raimundo J, Fyodor Kondrashov, and Kseniia Khudiakova.
“Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic
Interactions.” Bulletin of Mathematical Biology. Springer Nature, 2022.
https://doi.org/10.1007/s11538-022-01029-z.
ieee: R. J. Saona Urmeneta, F. Kondrashov, and K. Khudiakova, “Relation between
the number of peaks and the number of reciprocal sign epistatic interactions,”
Bulletin of Mathematical Biology, vol. 84, no. 8. Springer Nature, 2022.
ista: Saona Urmeneta RJ, Kondrashov F, Khudiakova K. 2022. Relation between the
number of peaks and the number of reciprocal sign epistatic interactions. Bulletin
of Mathematical Biology. 84(8), 74.
mla: Saona Urmeneta, Raimundo J., et al. “Relation between the Number of Peaks and
the Number of Reciprocal Sign Epistatic Interactions.” Bulletin of Mathematical
Biology, vol. 84, no. 8, 74, Springer Nature, 2022, doi:10.1007/s11538-022-01029-z.
short: R.J. Saona Urmeneta, F. Kondrashov, K. Khudiakova, Bulletin of Mathematical
Biology 84 (2022).
date_created: 2022-06-17T16:16:15Z
date_published: 2022-06-17T00:00:00Z
date_updated: 2023-08-03T07:20:53Z
day: '17'
ddc:
- '510'
- '570'
department:
- _id: GradSch
- _id: NiBa
- _id: JaMa
doi: 10.1007/s11538-022-01029-z
ec_funded: 1
external_id:
isi:
- '000812509800001'
file:
- access_level: open_access
checksum: 05a1fe7d10914a00c2bca9b447993a65
content_type: application/pdf
creator: dernst
date_created: 2022-06-20T07:51:32Z
date_updated: 2022-06-20T07:51:32Z
file_id: '11455'
file_name: 2022_BulletinMathBiology_Saona.pdf
file_size: 463025
relation: main_file
success: 1
file_date_updated: 2022-06-20T07:51:32Z
has_accepted_license: '1'
intvolume: ' 84'
isi: 1
issue: '8'
keyword:
- Computational Theory and Mathematics
- General Agricultural and Biological Sciences
- Pharmacology
- General Environmental Science
- General Biochemistry
- Genetics and Molecular Biology
- General Mathematics
- Immunology
- General Neuroscience
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 26580278-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '771209'
name: Characterizing the fitness landscape on population and global scales
- _id: c098eddd-5a5b-11eb-8a69-abe27170a68f
grant_number: I05127
name: Evolutionary analysis of gene regulation
publication: Bulletin of Mathematical Biology
publication_identifier:
eissn:
- 1522-9602
issn:
- 0092-8240
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- relation: erratum
url: https://doi.org/10.1007/s11538-022-01118-z
scopus_import: '1'
status: public
title: Relation between the number of peaks and the number of reciprocal sign epistatic
interactions
tmp:
image: /images/cc_by.png
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short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 84
year: '2022'
...
---
_id: '11700'
abstract:
- lang: eng
text: This paper contains two contributions in the study of optimal transport on
metric graphs. Firstly, we prove a Benamou–Brenier formula for the Wasserstein
distance, which establishes the equivalence of static and dynamical optimal transport.
Secondly, in the spirit of Jordan–Kinderlehrer–Otto, we show that McKean–Vlasov
equations can be formulated as gradient flow of the free energy in the Wasserstein
space of probability measures. The proofs of these results are based on careful
regularisation arguments to circumvent some of the difficulties arising in metric
graphs, namely, branching of geodesics and the failure of semi-convexity of entropy
functionals in the Wasserstein space.
acknowledgement: "ME acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG),
Grant SFB 1283/2 2021 – 317210226. DF and JM were supported by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 716117). JM also acknowledges support by the Austrian Science
Fund (FWF), Project SFB F65. The work of DM was partially supported by the Deutsche
Forschungsgemeinschaft\r\n(DFG), Grant 397230547. This article is based upon work
from COST Action\r\n18232 MAT-DYN-NET, supported by COST (European Cooperation in
Science\r\nand Technology), www.cost.eu. We wish to thank Martin Burger and Jan-Frederik\r\nPietschmann
for useful discussions. We are grateful to the anonymous referees for\r\ntheir careful
reading and useful suggestions."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Matthias
full_name: Erbar, Matthias
last_name: Erbar
- first_name: Dominik L
full_name: Forkert, Dominik L
id: 35C79D68-F248-11E8-B48F-1D18A9856A87
last_name: Forkert
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Delio
full_name: Mugnolo, Delio
last_name: Mugnolo
citation:
ama: Erbar M, Forkert DL, Maas J, Mugnolo D. Gradient flow formulation of diffusion
equations in the Wasserstein space over a metric graph. Networks and Heterogeneous
Media. 2022;17(5):687-717. doi:10.3934/nhm.2022023
apa: Erbar, M., Forkert, D. L., Maas, J., & Mugnolo, D. (2022). Gradient flow
formulation of diffusion equations in the Wasserstein space over a metric graph.
Networks and Heterogeneous Media. American Institute of Mathematical Sciences.
https://doi.org/10.3934/nhm.2022023
chicago: Erbar, Matthias, Dominik L Forkert, Jan Maas, and Delio Mugnolo. “Gradient
Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric
Graph.” Networks and Heterogeneous Media. American Institute of Mathematical
Sciences, 2022. https://doi.org/10.3934/nhm.2022023.
ieee: M. Erbar, D. L. Forkert, J. Maas, and D. Mugnolo, “Gradient flow formulation
of diffusion equations in the Wasserstein space over a metric graph,” Networks
and Heterogeneous Media, vol. 17, no. 5. American Institute of Mathematical
Sciences, pp. 687–717, 2022.
ista: Erbar M, Forkert DL, Maas J, Mugnolo D. 2022. Gradient flow formulation of
diffusion equations in the Wasserstein space over a metric graph. Networks and
Heterogeneous Media. 17(5), 687–717.
mla: Erbar, Matthias, et al. “Gradient Flow Formulation of Diffusion Equations in
the Wasserstein Space over a Metric Graph.” Networks and Heterogeneous Media,
vol. 17, no. 5, American Institute of Mathematical Sciences, 2022, pp. 687–717,
doi:10.3934/nhm.2022023.
short: M. Erbar, D.L. Forkert, J. Maas, D. Mugnolo, Networks and Heterogeneous Media
17 (2022) 687–717.
date_created: 2022-07-31T22:01:46Z
date_published: 2022-10-01T00:00:00Z
date_updated: 2023-08-03T12:25:49Z
day: '01'
department:
- _id: JaMa
doi: 10.3934/nhm.2022023
ec_funded: 1
external_id:
arxiv:
- '2105.05677'
isi:
- '000812422100001'
intvolume: ' 17'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.05677
month: '10'
oa: 1
oa_version: Preprint
page: 687-717
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Networks and Heterogeneous Media
publication_identifier:
eissn:
- 1556-181X
issn:
- 1556-1801
publication_status: published
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gradient flow formulation of diffusion equations in the Wasserstein space over
a metric graph
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 17
year: '2022'
...
---
_id: '11739'
abstract:
- lang: eng
text: We consider finite-volume approximations of Fokker--Planck equations on bounded
convex domains in $\mathbb{R}^d$ and study the corresponding gradient flow structures.
We reprove the convergence of the discrete to continuous Fokker--Planck equation
via the method of evolutionary $\Gamma$-convergence, i.e., we pass to the limit
at the level of the gradient flow structures, generalizing the one-dimensional
result obtained by Disser and Liero. The proof is of variational nature and relies
on a Mosco convergence result for functionals in the discrete-to-continuum limit
that is of independent interest. Our results apply to arbitrary regular meshes,
even though the associated discrete transport distances may fail to converge to
the Wasserstein distance in this generality.
acknowledgement: This work was supported by the European Research Council (ERC) under
the European Union's Horizon 2020 Research and Innovation Programme grant 716117
and by the AustrianScience Fund (FWF) through grants F65 and W1245.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dominik L
full_name: Forkert, Dominik L
id: 35C79D68-F248-11E8-B48F-1D18A9856A87
last_name: Forkert
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Forkert DL, Maas J, Portinale L. Evolutionary $\Gamma$-convergence of entropic
gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM
Journal on Mathematical Analysis. 2022;54(4):4297-4333. doi:10.1137/21M1410968
apa: Forkert, D. L., Maas, J., & Portinale, L. (2022). Evolutionary $\Gamma$-convergence
of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions.
SIAM Journal on Mathematical Analysis. Society for Industrial and Applied
Mathematics. https://doi.org/10.1137/21M1410968
chicago: Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\Gamma$-Convergence
of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.”
SIAM Journal on Mathematical Analysis. Society for Industrial and Applied
Mathematics, 2022. https://doi.org/10.1137/21M1410968.
ieee: D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\Gamma$-convergence
of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,”
SIAM Journal on Mathematical Analysis, vol. 54, no. 4. Society for Industrial
and Applied Mathematics, pp. 4297–4333, 2022.
ista: Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\Gamma$-convergence of
entropic gradient flow structures for Fokker-Planck equations in multiple dimensions.
SIAM Journal on Mathematical Analysis. 54(4), 4297–4333.
mla: Forkert, Dominik L., et al. “Evolutionary $\Gamma$-Convergence of Entropic
Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.”
SIAM Journal on Mathematical Analysis, vol. 54, no. 4, Society for Industrial
and Applied Mathematics, 2022, pp. 4297–333, doi:10.1137/21M1410968.
short: D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis
54 (2022) 4297–4333.
date_created: 2022-08-07T22:01:59Z
date_published: 2022-07-18T00:00:00Z
date_updated: 2023-08-03T12:37:21Z
day: '18'
department:
- _id: JaMa
doi: 10.1137/21M1410968
ec_funded: 1
external_id:
arxiv:
- '2008.10962'
isi:
- '000889274600001'
intvolume: ' 54'
isi: 1
issue: '4'
keyword:
- Fokker--Planck equation
- gradient flow
- evolutionary $\Gamma$-convergence
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2008.10962'
month: '07'
oa: 1
oa_version: Preprint
page: 4297-4333
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
name: Dissipation and Dispersion in Nonlinear Partial Differential Equations
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
related_material:
record:
- id: '10022'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Evolutionary $\Gamma$-convergence of entropic gradient flow structures for
Fokker-Planck equations in multiple dimensions
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...
---
_id: '10588'
abstract:
- lang: eng
text: We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying
the quasi curvature-dimension condition recently introduced in Milman (Commun
Pure Appl Math, to appear). We provide several applications to properties of the
corresponding heat semigroup. In particular, under the additional assumption of
infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the
heat semigroup with respect to the distance, and prove the irreducibility of the
heat semigroup. These results apply in particular to large classes of (ideal)
sub-Riemannian manifolds.
acknowledgement: "The authors are grateful to Dr. Bang-Xian Han for helpful discussions
on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor
Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino
Antonelli for reading a preliminary version of this work and for their valuable
comments and suggestions. Finally, they wish to express their gratitude to two anonymous
Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S.
gratefully acknowledges funding of his position by the Austrian Science Fund (FWF)
grant F65, and by the European Research Council (ERC, grant No. 716117, awarded
to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS
Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research
Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research
on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number
17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Kohei
full_name: Suzuki, Kohei
last_name: Suzuki
citation:
ama: Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and
applications. Mathematische Annalen. 2022;384:1815-1832. doi:10.1007/s00208-021-02331-2
apa: Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on
QCD- spaces and applications. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-021-02331-2
chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property
on QCD- Spaces and Applications.” Mathematische Annalen. Springer Nature,
2022. https://doi.org/10.1007/s00208-021-02331-2.
ieee: L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces
and applications,” Mathematische Annalen, vol. 384. Springer Nature, pp.
1815–1832, 2022.
ista: Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces
and applications. Mathematische Annalen. 384, 1815–1832.
mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on
QCD- Spaces and Applications.” Mathematische Annalen, vol. 384, Springer
Nature, 2022, pp. 1815–32, doi:10.1007/s00208-021-02331-2.
short: L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.
date_created: 2022-01-02T23:01:35Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-02T13:39:05Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00208-021-02331-2
ec_funded: 1
external_id:
arxiv:
- '2110.05137'
isi:
- '000734150200001'
file:
- access_level: open_access
checksum: 2593abbf195e38efa93b6006b1e90eb1
content_type: application/pdf
creator: alisjak
date_created: 2022-01-03T11:08:31Z
date_updated: 2022-01-03T11:08:31Z
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file_name: 2021_MathAnn_DelloSchiavo.pdf
file_size: 410090
relation: main_file
success: 1
file_date_updated: 2022-01-03T11:08:31Z
has_accepted_license: '1'
intvolume: ' 384'
isi: 1
keyword:
- quasi curvature-dimension condition
- sub-riemannian geometry
- Sobolev-to-Lipschitz property
- Varadhan short-time asymptotics
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 1815-1832
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Mathematische Annalen
publication_identifier:
eissn:
- 1432-1807
issn:
- 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sobolev-to-Lipschitz property on QCD- spaces and applications
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 384
year: '2022'
...
---
_id: '11916'
abstract:
- lang: eng
text: A domain is called Kac regular for a quadratic form on L2 if every functions
vanishing almost everywhere outside the domain can be approximated in form norm
by functions with compact support in the domain. It is shown that this notion
is stable under domination of quadratic forms. As applications measure perturbations
of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and
Schrödinger operators on manifolds are studied. Along the way a characterization
of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally
Riemannian metric measure spaces is obtained.
acknowledgement: "The author was supported by the German Academic Scholarship Foundation
(Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG)
via RTG 1523/2. The author would like to thank Daniel Lenz for his support and encouragement
during the author’s ongoing graduate studies and him as well as Marcel Schmidt for
fruitful discussions on domination of quadratic forms. He wants to thank Batu Güneysu
and Peter Stollmann for valuable comments on a preliminary version of this article.
He would also like to thank the organizers of the conference Analysis and Geometry
on Graphs and Manifolds in Potsdam, where the initial motivation of this article
was conceived, and the organizers of the intense activity period Metric Measure
Spaces and Ricci Curvature at MPIM in Bonn, where this work was finished.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria)."
article_number: '38'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Wirth M. Kac regularity and domination of quadratic forms. Advances in Operator
Theory. 2022;7(3). doi:10.1007/s43036-022-00199-w
apa: Wirth, M. (2022). Kac regularity and domination of quadratic forms. Advances
in Operator Theory. Springer Nature. https://doi.org/10.1007/s43036-022-00199-w
chicago: Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” Advances
in Operator Theory. Springer Nature, 2022. https://doi.org/10.1007/s43036-022-00199-w.
ieee: M. Wirth, “Kac regularity and domination of quadratic forms,” Advances
in Operator Theory, vol. 7, no. 3. Springer Nature, 2022.
ista: Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances
in Operator Theory. 7(3), 38.
mla: Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” Advances
in Operator Theory, vol. 7, no. 3, 38, Springer Nature, 2022, doi:10.1007/s43036-022-00199-w.
short: M. Wirth, Advances in Operator Theory 7 (2022).
date_created: 2022-08-18T07:22:24Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-02-21T10:08:07Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s43036-022-00199-w
file:
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checksum: 913474844a1b38264fb710746d5e2e98
content_type: application/pdf
creator: dernst
date_created: 2022-08-18T08:02:34Z
date_updated: 2022-08-18T08:02:34Z
file_id: '11921'
file_name: 2022_AdvancesOperatorTheory_Wirth.pdf
file_size: 389060
relation: main_file
success: 1
file_date_updated: 2022-08-18T08:02:34Z
has_accepted_license: '1'
intvolume: ' 7'
issue: '3'
keyword:
- Algebra and Number Theory
- Analysis
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: Advances in Operator Theory
publication_identifier:
eissn:
- 2538-225X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Kac regularity and domination of quadratic forms
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2022'
...