---
_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
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: 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: '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:
- access_level: open_access
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'
...
---
_id: '10023'
abstract:
- lang: eng
text: We study the temporal dissipation of variance and relative entropy for ergodic
Markov Chains in continuous time, and compute explicitly the corresponding dissipation
rates. These are identified, as is well known, in the case of the variance in
terms of an appropriate Hilbertian norm; and in the case of the relative entropy,
in terms of a Dirichlet form which morphs into a version of the familiar Fisher
information under conditions of detailed balance. Here we obtain trajectorial
versions of these results, valid along almost every path of the random motion
and most transparent in the backwards direction of time. Martingale arguments
and time reversal play crucial roles, as in the recent work of Karatzas, Schachermayer
and Tschiderer for conservative diffusions. Extensions are developed to general
“convex divergences” and to countable state-spaces. The steepest descent and gradient
flow properties for the variance, the relative entropy, and appropriate generalizations,
are studied along with their respective geometries under conditions of detailed
balance, leading to a very direct proof for the HWI inequality of Otto and Villani
in the present context.
acknowledgement: I.K. acknowledges support from the U.S. National Science Foundation
under Grant NSF-DMS-20-04997. J.M. 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 project
F65. W.S. acknowledges support from the Austrian Science Fund (FWF) under grant
P28861 and by the Vienna Science and Technology Fund (WWTF) through projects MA14-008
and MA16-021.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ioannis
full_name: Karatzas, Ioannis
last_name: Karatzas
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Walter
full_name: Schachermayer, Walter
last_name: Schachermayer
citation:
ama: Karatzas I, Maas J, Schachermayer W. Trajectorial dissipation and gradient
flow for the relative entropy in Markov chains. Communications in Information
and Systems. 2021;21(4):481-536. doi:10.4310/CIS.2021.v21.n4.a1
apa: Karatzas, I., Maas, J., & Schachermayer, W. (2021). Trajectorial dissipation
and gradient flow for the relative entropy in Markov chains. Communications
in Information and Systems. International Press. https://doi.org/10.4310/CIS.2021.v21.n4.a1
chicago: Karatzas, Ioannis, Jan Maas, and Walter Schachermayer. “Trajectorial Dissipation
and Gradient Flow for the Relative Entropy in Markov Chains.” Communications
in Information and Systems. International Press, 2021. https://doi.org/10.4310/CIS.2021.v21.n4.a1.
ieee: I. Karatzas, J. Maas, and W. Schachermayer, “Trajectorial dissipation and
gradient flow for the relative entropy in Markov chains,” Communications in
Information and Systems, vol. 21, no. 4. International Press, pp. 481–536,
2021.
ista: Karatzas I, Maas J, Schachermayer W. 2021. Trajectorial dissipation and gradient
flow for the relative entropy in Markov chains. Communications in Information
and Systems. 21(4), 481–536.
mla: Karatzas, Ioannis, et al. “Trajectorial Dissipation and Gradient Flow for the
Relative Entropy in Markov Chains.” Communications in Information and Systems,
vol. 21, no. 4, International Press, 2021, pp. 481–536, doi:10.4310/CIS.2021.v21.n4.a1.
short: I. Karatzas, J. Maas, W. Schachermayer, Communications in Information and
Systems 21 (2021) 481–536.
date_created: 2021-09-19T08:53:19Z
date_published: 2021-06-04T00:00:00Z
date_updated: 2021-09-20T12:51:18Z
day: '04'
department:
- _id: JaMa
doi: 10.4310/CIS.2021.v21.n4.a1
ec_funded: 1
external_id:
arxiv:
- '2005.14177'
intvolume: ' 21'
issue: '4'
keyword:
- Markov Chain
- relative entropy
- time reversal
- steepest descent
- gradient flow
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2005.14177
month: '06'
oa: 1
oa_version: Preprint
page: 481-536
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: Communications in Information and Systems
publication_identifier:
issn:
- 1526-7555
publication_status: published
publisher: International Press
quality_controlled: '1'
status: public
title: Trajectorial dissipation and gradient flow for the relative entropy in Markov
chains
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 21
year: '2021'
...
---
_id: '10024'
abstract:
- lang: eng
text: In this paper, we introduce a random environment for the exclusion process
in obtained by assigning a maximal occupancy to each site. This maximal occupancy
is allowed to randomly vary among sites, and partial exclusion occurs. Under the
assumption of ergodicity under translation and uniform ellipticity of the environment,
we derive a quenched hydrodynamic limit in path space by strengthening the mild
solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose,
we prove, employing the technology developed for the random conductance model,
a homogenization result in the form of an arbitrary starting point quenched invariance
principle for a single particle in the same environment, which is a result of
independent interest. The self-duality property of the partial exclusion process
allows us to transfer this homogenization result to the particle system and, then,
apply the tightness criterion in Redig et al. (2020).
acknowledgement: The authors would like to thank Marek Biskup and Alberto Chiarini
for useful suggestions and Cristian Giardina, Frank den Hollander and Shubhamoy Nandan for inspiring discussions. S.F. acknowledges Simona Villa for her help in creating the picture. Furthermore,
the authors thank two anonymous referees for the careful reading of the manuscript. S.F.
acknowledges financial support from NWO, The Netherlands via the grant TOP1.17.019.
F.S. acknowledges financial support from NWO via the TOP1 grant 613.001.552 as well as
funding from the European Union’s Horizon 2020 research and innovation programme
under the Marie-Skłodowska-Curie grant agreement No. 754411.
article_processing_charge: Yes
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. Hydrodynamics for the partial exclusion process
in random environment. Stochastic Processes and their Applications. 2021;142:124-158.
doi:10.1016/j.spa.2021.08.006
apa: Floreani, S., Redig, F., & Sau, F. (2021). Hydrodynamics for the partial
exclusion process in random environment. Stochastic Processes and Their Applications.
Elsevier. https://doi.org/10.1016/j.spa.2021.08.006
chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the
Partial Exclusion Process in Random Environment.” Stochastic Processes and
Their Applications. Elsevier, 2021. https://doi.org/10.1016/j.spa.2021.08.006.
ieee: S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion
process in random environment,” Stochastic Processes and their Applications,
vol. 142. Elsevier, pp. 124–158, 2021.
ista: Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion
process in random environment. Stochastic Processes and their Applications. 142,
124–158.
mla: Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in
Random Environment.” Stochastic Processes and Their Applications, vol.
142, Elsevier, 2021, pp. 124–58, doi:10.1016/j.spa.2021.08.006.
short: S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications
142 (2021) 124–158.
date_created: 2021-09-19T22:01:25Z
date_published: 2021-08-27T00:00:00Z
date_updated: 2023-08-14T06:52:43Z
day: '27'
ddc:
- '519'
department:
- _id: JaMa
doi: 10.1016/j.spa.2021.08.006
ec_funded: 1
external_id:
arxiv:
- '1911.12564'
isi:
- '000697748500005'
file:
- access_level: open_access
checksum: 56768c553d7218ee5714902ffec90ec4
content_type: application/pdf
creator: dernst
date_created: 2022-05-13T07:55:50Z
date_updated: 2022-05-13T07:55:50Z
file_id: '11370'
file_name: 2021_StochasticProcessesAppl_Floreani.pdf
file_size: 2115791
relation: main_file
success: 1
file_date_updated: 2022-05-13T07:55:50Z
has_accepted_license: '1'
intvolume: ' 142'
isi: 1
keyword:
- hydrodynamic limit
- random environment
- random conductance model
- arbitrary starting point quenched invariance principle
- duality
- mild solution
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 124-158
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Stochastic Processes and their Applications
publication_identifier:
issn:
- 0304-4149
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hydrodynamics for the partial exclusion process in random environment
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: 142
year: '2021'
...
---
_id: '10030'
abstract:
- lang: eng
text: "This PhD thesis is primarily focused on the study of discrete transport problems,
introduced for the first time in the seminal works of Maas [Maa11] and Mielke
[Mie11] on finite state Markov chains and reaction-diffusion equations, respectively.
More in detail, my research focuses on the study of transport costs on graphs,
in particular the convergence and the stability of such problems in the discrete-to-continuum
limit. This thesis also includes some results concerning\r\nnon-commutative optimal
transport. The first chapter of this thesis consists of a general introduction
to the optimal transport problems, both in the discrete, the continuous, and the
non-commutative setting. Chapters 2 and 3 present the content of two works, obtained
in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have
been able to show the convergence of discrete transport costs on periodic graphs
to suitable continuous ones, which can be described by means of a homogenisation
result. We first focus on the particular case of quadratic costs on the real line
and then extending the result to more general costs in arbitrary dimension. Our
results are the first complete characterisation of limits of transport costs on
periodic graphs in arbitrary dimension which do not rely on any additional symmetry.
In Chapter 4 we turn our attention to one of the intriguing connection between
evolution equations and optimal transport, represented by the theory of gradient
flows. We show that discrete gradient flow structures associated to a finite volume
approximation of a certain class of diffusive equations (Fokker–Planck) is stable
in the limit of vanishing meshes, reproving the convergence of the scheme via
the method of evolutionary Γ-convergence and exploiting a more variational point
of view on the problem. This is based on a collaboration with Dominik Forkert
and Jan Maas. Chapter 5 represents a change of perspective, moving away from the
discrete world and reaching the non-commutative one. As in the discrete case,
we discuss how classical tools coming from the commutative optimal transport can
be translated into the setting of density matrices. In particular, in this final
chapter we present a non-commutative version of the Schrödinger problem (or entropic
regularised optimal transport problem) and discuss existence and characterisation
of minimisers, a duality result, and present a non-commutative version of the
well-known Sinkhorn algorithm to compute the above mentioned optimisers. This
is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally,
Appendix A and B contain some additional material and discussions, with particular
attention to Harnack inequalities and the regularity of flows on discrete spaces."
acknowledged_ssus:
- _id: M-Shop
- _id: NanoFab
acknowledgement: The author gratefully acknowledges support by the Austrian Science
Fund (FWF), grants No W1245.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Portinale L. Discrete-to-continuum limits of transport problems and gradient
flows in the space of measures. 2021. doi:10.15479/at:ista:10030
apa: Portinale, L. (2021). Discrete-to-continuum limits of transport problems
and gradient flows in the space of measures. Institute of Science and Technology
Austria. https://doi.org/10.15479/at:ista:10030
chicago: Portinale, Lorenzo. “Discrete-to-Continuum Limits of Transport Problems
and Gradient Flows in the Space of Measures.” Institute of Science and Technology
Austria, 2021. https://doi.org/10.15479/at:ista:10030.
ieee: L. Portinale, “Discrete-to-continuum limits of transport problems and gradient
flows in the space of measures,” Institute of Science and Technology Austria,
2021.
ista: Portinale L. 2021. Discrete-to-continuum limits of transport problems and
gradient flows in the space of measures. Institute of Science and Technology Austria.
mla: Portinale, Lorenzo. Discrete-to-Continuum Limits of Transport Problems and
Gradient Flows in the Space of Measures. Institute of Science and Technology
Austria, 2021, doi:10.15479/at:ista:10030.
short: L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient
Flows in the Space of Measures, Institute of Science and Technology Austria, 2021.
date_created: 2021-09-21T09:14:15Z
date_published: 2021-09-22T00:00:00Z
date_updated: 2023-09-07T13:31:06Z
day: '22'
ddc:
- '515'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JaMa
doi: 10.15479/at:ista:10030
file:
- access_level: closed
checksum: 8cd60dcb8762e8f21867e21e8001e183
content_type: application/x-zip-compressed
creator: cchlebak
date_created: 2021-09-21T09:17:34Z
date_updated: 2022-03-10T12:14:42Z
file_id: '10032'
file_name: tex_and_pictures.zip
file_size: 3876668
relation: source_file
- access_level: open_access
checksum: 9789e9d967c853c1503ec7f307170279
content_type: application/pdf
creator: cchlebak
date_created: 2021-09-27T11:14:31Z
date_updated: 2021-09-27T11:14:31Z
file_id: '10047'
file_name: thesis_portinale_Final (1).pdf
file_size: 2532673
relation: main_file
file_date_updated: 2022-03-10T12:14:42Z
has_accepted_license: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
name: Dissipation and Dispersion in Nonlinear Partial Differential Equations
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10022'
relation: part_of_dissertation
status: public
- id: '9792'
relation: part_of_dissertation
status: public
- id: '7573'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: Discrete-to-continuum limits of transport problems and gradient flows in the
space of measures
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: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '10070'
abstract:
- lang: eng
text: We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties
for generalized intrinsic distances on strongly local Dirichlet spaces possibly
without square field operator. We present many non-smooth and infinite-dimensional
examples. As an application, we prove the integral Varadhan short-time asymptotic
with respect to a given distance function for a large class of strongly local
Dirichlet forms.
acknowledgement: 'The authors are grateful to Professor Kazuhiro Kuwae for kindly
providing a copy of [49]. They are also grateful to Dr. Bang-Xian Han for helpful
discussions on the Sobolev-to-Lipschitz property on metric measure spaces. They
wish to express their deepest gratitude to an anonymous Reviewer, whose punctual
remarks and comments greatly improved the accessibility and overall quality of the
initial submission. This work was completed while L.D.S. was a member of the Institut
für Angewandte Mathematik of the University of Bonn. He acknowledges funding of
his position at that time by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) through the Sonderforschungsbereich (Sfb, Collaborative Research Center)
1060 - project number 211504053. He also acknowledges funding of his current 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). K.S. gratefully acknowledges
funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier
International Research Center Initiative (WPI), MEXT, Japan; and JSPS Grant-in-Aid
for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials
Design”, Grant Number 17H06465.'
article_number: '109234'
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
- first_name: Kohei
full_name: Suzuki, Kohei
last_name: Suzuki
citation:
ama: Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
2021;281(11). doi:10.1016/j.jfa.2021.109234
apa: Dello Schiavo, L., & Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2021.109234
chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and
Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal
of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109234.
ieee: L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces,” Journal of Functional Analysis,
vol. 281, no. 11. Elsevier, 2021.
ista: Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
281(11), 109234.
mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz
Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis,
vol. 281, no. 11, 109234, Elsevier, 2021, doi:10.1016/j.jfa.2021.109234.
short: L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).
date_created: 2021-10-03T22:01:21Z
date_published: 2021-09-15T00:00:00Z
date_updated: 2023-08-14T07:05:44Z
day: '15'
department:
- _id: JaMa
doi: 10.1016/j.jfa.2021.109234
ec_funded: 1
external_id:
arxiv:
- '2008.01492'
isi:
- '000703896600005'
intvolume: ' 281'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2008.01492
month: '09'
oa: 1
oa_version: Preprint
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 Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local
Dirichlet spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 281
year: '2021'
...
---
_id: '10613'
abstract:
- lang: eng
text: Motivated by the recent preprint [\emph{arXiv:2004.08412}] by Ayala, Carinci,
and Redig, we first provide a general framework for the study of scaling limits
of higher-order fields. Then, by considering the same class of infinite interacting
particle systems as in [\emph{arXiv:2004.08412}], namely symmetric simple exclusion
and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic
limit, and convergence for the equilibrium fluctuations, of higher-order fields.
In particular, the limit fields exhibit a tensor structure. Our fluctuation result
differs from that in [\emph{arXiv:2004.08412}], since we considered-dimensional
Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium
fluctuations, of higher-order fields. In particular, the limit fields exhibit
a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}],
since we consider a different notion of higher-order fluctuation fields.
acknowledgement: "F.S. would like to thank Mario Ayala and Frank Redig for useful
discussions. J.P.C. acknowledges partial financial support from the US National
Science Foundation (DMS-1855604). F.S. was financially supported by the European
Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie
grant agreement No. 754411.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Joe P.
full_name: Chen, Joe P.
last_name: Chen
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: Chen JP, Sau F. Higher-order hydrodynamics and equilibrium fluctuations of
interacting particle systems. Markov Processes And Related Fields. 2021;27(3):339-380.
apa: Chen, J. P., & Sau, F. (2021). Higher-order hydrodynamics and equilibrium
fluctuations of interacting particle systems. Markov Processes And Related
Fields. Polymat Publishing.
chicago: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium
Fluctuations of Interacting Particle Systems.” Markov Processes And Related
Fields. Polymat Publishing, 2021.
ieee: J. P. Chen and F. Sau, “Higher-order hydrodynamics and equilibrium fluctuations
of interacting particle systems,” Markov Processes And Related Fields,
vol. 27, no. 3. Polymat Publishing, pp. 339–380, 2021.
ista: Chen JP, Sau F. 2021. Higher-order hydrodynamics and equilibrium fluctuations
of interacting particle systems. Markov Processes And Related Fields. 27(3), 339–380.
mla: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium
Fluctuations of Interacting Particle Systems.” Markov Processes And Related
Fields, vol. 27, no. 3, Polymat Publishing, 2021, pp. 339–80.
short: J.P. Chen, F. Sau, Markov Processes And Related Fields 27 (2021) 339–380.
date_created: 2022-01-10T14:02:31Z
date_published: 2021-03-16T00:00:00Z
date_updated: 2022-01-10T15:29:08Z
day: '16'
department:
- _id: JaMa
ec_funded: 1
external_id:
arxiv:
- '2008.13403'
intvolume: ' 27'
issue: '3'
keyword:
- interacting particle systems
- higher-order fields
- hydrodynamic limit
- equilibrium fluctuations
- duality
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2008.13403
month: '03'
oa: 1
oa_version: Preprint
page: 339-380
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Markov Processes And Related Fields
publication_identifier:
issn:
- 1024-2953
publication_status: published
publisher: Polymat Publishing
quality_controlled: '1'
related_material:
link:
- description: Link to Abstract on publisher's website
relation: other
url: http://math-mprf.org/journal/articles/id1614/
- description: Referred to in Abstract
relation: used_for_analysis_in
url: https://arxiv.org/abs/2004.08412
status: public
title: Higher-order hydrodynamics and equilibrium fluctuations of interacting particle
systems
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 27
year: '2021'
...
---
_id: '9627'
abstract:
- lang: eng
text: "We compute the deficiency spaces of operators of the form \U0001D43B\U0001D434⊗̂
\U0001D43C+\U0001D43C⊗̂ \U0001D43B\U0001D435, for symmetric \U0001D43B\U0001D434
and self-adjoint \U0001D43B\U0001D435. This enables us to construct self-adjoint
extensions (if they exist) by means of von Neumann's theory. The structure of
the deficiency spaces for this case was asserted already in Ibort et al. [Boundary
dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301],
but only proven under the restriction of \U0001D43B\U0001D435 having discrete,
non-degenerate spectrum."
acknowledgement: M. W. gratefully acknowledges financial support by the German Academic
Scholarship Foundation (Studienstiftung des deutschen Volkes). T.W. thanks PAO Gazprom
Neft, the Euler International Mathematical Institute in Saint Petersburg and ORISA
GmbH for their financial support in the form of scholarships during his Master's
and Bachelor's studies respectively. The authors want to thank Mark Malamud for
pointing out the reference [1] to them. This work was supported by the Ministry
of Science and Higher Education of the Russian Federation, agreement No 075-15-2019-1619.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Daniel
full_name: Lenz, Daniel
last_name: Lenz
- first_name: Timon
full_name: Weinmann, Timon
last_name: Weinmann
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians.
Proceedings of the Edinburgh Mathematical Society. 2021;64(3):443-447.
doi:10.1017/S0013091521000080
apa: Lenz, D., Weinmann, T., & Wirth, M. (2021). Self-adjoint extensions of
bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society.
Cambridge University Press. https://doi.org/10.1017/S0013091521000080
chicago: Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions
of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society.
Cambridge University Press, 2021. https://doi.org/10.1017/S0013091521000080.
ieee: D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite
Hamiltonians,” Proceedings of the Edinburgh Mathematical Society, vol.
64, no. 3. Cambridge University Press, pp. 443–447, 2021.
ista: Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians.
Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.
mla: Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings
of the Edinburgh Mathematical Society, vol. 64, no. 3, Cambridge University
Press, 2021, pp. 443–47, doi:10.1017/S0013091521000080.
short: D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical
Society 64 (2021) 443–447.
date_created: 2021-07-04T22:01:24Z
date_published: 2021-08-01T00:00:00Z
date_updated: 2023-08-17T07:12:05Z
day: '01'
department:
- _id: JaMa
doi: 10.1017/S0013091521000080
external_id:
arxiv:
- '1912.03670'
isi:
- '000721363700003'
intvolume: ' 64'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1017/S0013091521000080
month: '08'
oa: 1
oa_version: Published Version
page: 443-447
publication: Proceedings of the Edinburgh Mathematical Society
publication_identifier:
eissn:
- 1464-3839
issn:
- 0013-0915
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Self-adjoint extensions of bipartite Hamiltonians
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2021'
...
---
_id: '9733'
abstract:
- lang: eng
text: This thesis is the result of the research carried out by the author during
his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich
polaron model, specifically to its regime of strong coupling. This model, which
is rigorously introduced and discussed in the introduction, has been of great
interest in condensed matter physics and field theory for more than eighty years.
It is used to describe an electron interacting with the atoms of a solid material
(the strength of this interaction is modeled by the presence of a coupling constant
α in the Hamiltonian of the system). The particular regime examined here, which
is mathematically described by considering the limit α →∞, displays many interesting
features related to the emergence of classical behavior, which allows for a simplified
effective description of the system under analysis. The properties, the range
of validity and a quantitative analysis of the precision of such classical approximations
are the main object of the present work. We specify our investigation to the study
of the ground state energy of the system, its dynamics and its effective mass.
For each of these problems, we provide in the introduction an overview of the
previously known results and a detailed account of the original contributions
by the author.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
citation:
ama: Feliciangeli D. The polaron at strong coupling. 2021. doi:10.15479/at:ista:9733
apa: Feliciangeli, D. (2021). The polaron at strong coupling. Institute of
Science and Technology Austria. https://doi.org/10.15479/at:ista:9733
chicago: Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science
and Technology Austria, 2021. https://doi.org/10.15479/at:ista:9733.
ieee: D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and
Technology Austria, 2021.
ista: Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science
and Technology Austria.
mla: Feliciangeli, Dario. The Polaron at Strong Coupling. Institute of Science
and Technology Austria, 2021, doi:10.15479/at:ista:9733.
short: D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and
Technology Austria, 2021.
date_created: 2021-07-27T15:48:30Z
date_published: 2021-08-20T00:00:00Z
date_updated: 2024-03-06T12:30:44Z
day: '20'
ddc:
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- '519'
- '539'
degree_awarded: PhD
department:
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- _id: RoSe
- _id: JaMa
doi: 10.15479/at:ista:9733
ec_funded: 1
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language:
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oa: 1
oa_version: Published Version
page: '180'
project:
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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: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
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status: public
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status: public
- id: '9225'
relation: part_of_dissertation
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- id: '9781'
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status: public
- id: '9791'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: The polaron at strong coupling
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type: dissertation
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year: '2021'
...
---
_id: '9792'
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 careful 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 thanks 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. Finally, the authors
also thanks J. Maas and R. Seiringer for their feedback and useful comments to a
first draft of the article. L.P. acknowledges support by the Austrian Science Fund
(FWF), grants No W1245 and NoF65. D.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 European
Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942].'
article_number: '2106.11217'
article_processing_charge: No
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. arXiv.
doi:10.48550/arXiv.2106.11217
apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (n.d.). A non-commutative
entropic optimal transport approach to quantum composite systems at positive temperature.
arXiv. https://doi.org/10.48550/arXiv.2106.11217
chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative
Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2106.11217.
ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic
optimal transport approach to quantum composite systems at positive temperature,”
arXiv. .
ista: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal
transport approach to quantum composite systems at positive temperature. arXiv,
2106.11217.
mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach
to Quantum Composite Systems at Positive Temperature.” ArXiv, 2106.11217,
doi:10.48550/arXiv.2106.11217.
short: D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.).
date_created: 2021-08-06T09:07:12Z
date_published: 2021-07-21T00:00:00Z
date_updated: 2023-11-14T13:21:01Z
day: '21'
ddc:
- '510'
department:
- _id: RoSe
- _id: JaMa
doi: 10.48550/arXiv.2106.11217
ec_funded: 1
external_id:
arxiv:
- '2106.11217'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.48550/arXiv.2106.11217
month: '07'
oa: 1
oa_version: Preprint
project:
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call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _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: arXiv
publication_status: submitted
related_material:
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status: public
- id: '10030'
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status: public
title: A non-commutative entropic optimal transport approach to quantum composite
systems at positive temperature
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: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9973'
abstract:
- lang: eng
text: In this article we introduce a complete gradient estimate for symmetric quantum
Markov semigroups on von Neumann algebras equipped with a normal faithful tracial
state, which implies semi-convexity of the entropy with respect to the recently
introduced noncommutative 2-Wasserstein distance. We show that this complete gradient
estimate is stable under tensor products and free products and establish its validity
for a number of examples. As an application we prove a complete modified logarithmic
Sobolev inequality with optimal constant for Poisson-type semigroups on free group
factors.
acknowledgement: Both authors would like to thank Jan Maas for fruitful discussions
and helpful comments.
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. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 2021;387:761–791. doi:10.1007/s00220-021-04199-4
apa: Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov
semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4
chicago: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” Communications in Mathematical Physics. Springer Nature,
2021. https://doi.org/10.1007/s00220-021-04199-4.
ieee: M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,”
Communications in Mathematical Physics, vol. 387. Springer Nature, pp.
761–791, 2021.
ista: Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 387, 761–791.
mla: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” Communications in Mathematical Physics, vol. 387, Springer
Nature, 2021, pp. 761–791, doi:10.1007/s00220-021-04199-4.
short: M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.
date_created: 2021-08-30T10:07:44Z
date_published: 2021-08-30T00:00:00Z
date_updated: 2023-08-11T11:09:07Z
day: '30'
ddc:
- '621'
department:
- _id: JaMa
doi: 10.1007/s00220-021-04199-4
ec_funded: 1
external_id:
arxiv:
- '2007.13506'
isi:
- '000691214200001'
file:
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checksum: 8a602f916b1c2b0dc1159708b7cb204b
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creator: cchlebak
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file_name: 2021_CommunMathPhys_Wirth.pdf
file_size: 505971
relation: main_file
file_date_updated: 2021-09-08T09:46:34Z
has_accepted_license: '1'
intvolume: ' 387'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 761–791
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Complete gradient estimates of 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 387
year: '2021'
...
---
_id: '8670'
abstract:
- lang: eng
text: The α–z Rényi relative entropies are a two-parameter family of Rényi relative
entropies that are quantum generalizations of the classical α-Rényi relative entropies.
In the work [Adv. Math. 365, 107053 (2020)], we decided the full range of (α,
z) for which the data processing inequality (DPI) is valid. In this paper, we
give algebraic conditions for the equality in DPI. For the full range of parameters
(α, z), we give necessary conditions and sufficient conditions. For most parameters,
we give equivalent conditions. This generalizes and strengthens the results of
Leditzky et al. [Lett. Math. Phys. 107, 61–80 (2017)].
acknowledgement: This research was supported by the European Union’s Horizon 2020
research and innovation program under the Marie Skłodowska-Curie Grant Agreement
No. 754411. The author would like to thank Anna Vershynina and Sarah Chehade for
their helpful comments.
article_number: '102201'
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. Equality conditions of data processing inequality for α-z Rényi relative
entropies. Journal of Mathematical Physics. 2020;61(10). doi:10.1063/5.0022787
apa: Zhang, H. (2020). Equality conditions of data processing inequality for α-z
Rényi relative entropies. Journal of Mathematical Physics. AIP Publishing.
https://doi.org/10.1063/5.0022787
chicago: Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z
Rényi Relative Entropies.” Journal of Mathematical Physics. AIP Publishing,
2020. https://doi.org/10.1063/5.0022787.
ieee: H. Zhang, “Equality conditions of data processing inequality for α-z Rényi
relative entropies,” Journal of Mathematical Physics, vol. 61, no. 10.
AIP Publishing, 2020.
ista: Zhang H. 2020. Equality conditions of data processing inequality for α-z Rényi
relative entropies. Journal of Mathematical Physics. 61(10), 102201.
mla: Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi
Relative Entropies.” Journal of Mathematical Physics, vol. 61, no. 10,
102201, AIP Publishing, 2020, doi:10.1063/5.0022787.
short: H. Zhang, Journal of Mathematical Physics 61 (2020).
date_created: 2020-10-18T22:01:36Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2023-08-22T10:32:29Z
day: '01'
department:
- _id: JaMa
doi: 10.1063/5.0022787
ec_funded: 1
external_id:
arxiv:
- '2007.06644'
isi:
- '000578529200001'
intvolume: ' 61'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2007.06644
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Mathematical Physics
publication_identifier:
issn:
- '00222488'
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equality conditions of data processing inequality for α-z Rényi relative entropies
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 61
year: '2020'
...
---
_id: '8758'
abstract:
- lang: eng
text: We consider various modeling levels for spatially homogeneous chemical reaction
systems, namely the chemical master equation, the chemical Langevin dynamics,
and the reaction-rate equation. Throughout we restrict our study to the case where
the microscopic system satisfies the detailed-balance condition. The latter allows
us to enrich the systems with a gradient structure, i.e. the evolution is given
by a gradient-flow equation. We present the arising links between the associated
gradient structures that are driven by the relative entropy of the detailed-balance
steady state. The limit of large volumes is studied in the sense of evolutionary
Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive
hybrid models for coupling different modeling levels.
acknowledgement: The research of A.M. was partially supported by the Deutsche Forschungsgemeinschaft
(DFG) via the Collaborative Research Center SFB 1114 Scaling Cascades in Complex
Systems (Project No. 235221301), through the Subproject C05 Effective models for
materials and interfaces with multiple scales. 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), and by the Austrian Science
Fund (FWF), Project SFB F65. The authors thank Christof Schütte, Robert I. A. Patterson,
and Stefanie Winkelmann for helpful and stimulating discussions. Open access funding
provided by Austrian Science Fund (FWF).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Alexander
full_name: Mielke, Alexander
last_name: Mielke
citation:
ama: Maas J, Mielke A. Modeling of chemical reaction systems with detailed balance
using gradient structures. Journal of Statistical Physics. 2020;181(6):2257-2303.
doi:10.1007/s10955-020-02663-4
apa: Maas, J., & Mielke, A. (2020). Modeling of chemical reaction systems with
detailed balance using gradient structures. Journal of Statistical Physics.
Springer Nature. https://doi.org/10.1007/s10955-020-02663-4
chicago: Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems
with Detailed Balance Using Gradient Structures.” Journal of Statistical Physics.
Springer Nature, 2020. https://doi.org/10.1007/s10955-020-02663-4.
ieee: J. Maas and A. Mielke, “Modeling of chemical reaction systems with detailed
balance using gradient structures,” Journal of Statistical Physics, vol.
181, no. 6. Springer Nature, pp. 2257–2303, 2020.
ista: Maas J, Mielke A. 2020. Modeling of chemical reaction systems with detailed
balance using gradient structures. Journal of Statistical Physics. 181(6), 2257–2303.
mla: Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with
Detailed Balance Using Gradient Structures.” Journal of Statistical Physics,
vol. 181, no. 6, Springer Nature, 2020, pp. 2257–303, doi:10.1007/s10955-020-02663-4.
short: J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303.
date_created: 2020-11-15T23:01:18Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2023-08-22T13:24:27Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s10955-020-02663-4
ec_funded: 1
external_id:
arxiv:
- '2004.02831'
isi:
- '000587107200002'
file:
- access_level: open_access
checksum: bc2b63a90197b97cbc73eccada4639f5
content_type: application/pdf
creator: dernst
date_created: 2021-02-04T10:29:11Z
date_updated: 2021-02-04T10:29:11Z
file_id: '9087'
file_name: 2020_JourStatPhysics_Maas.pdf
file_size: 753596
relation: main_file
success: 1
file_date_updated: 2021-02-04T10:29:11Z
has_accepted_license: '1'
intvolume: ' 181'
isi: 1
issue: '6'
language:
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month: '12'
oa: 1
oa_version: Published Version
page: 2257-2303
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: ' F06504'
name: Taming Complexity in Partial Di erential Systems
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: Modeling of chemical reaction systems with detailed balance using gradient
structures
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: 181
year: '2020'
...
---
_id: '8973'
abstract:
- lang: eng
text: We consider the symmetric simple exclusion process in Zd with quenched bounded
dynamic random conductances and prove its hydrodynamic limit in path space. The
main tool is the connection, due to the self-duality of the process, between the
invariance principle for single particles starting from all points and the macroscopic
behavior of the density field. While the hydrodynamic limit at fixed macroscopic
times is obtained via a generalization to the time-inhomogeneous context of the
strategy introduced in [41], in order to prove tightness for the sequence of empirical
density fields we develop a new criterion based on the notion of uniform conditional
stochastic continuity, following [50]. In conclusion, we show that uniform elliptic
dynamic conductances provide an example of environments in which the so-called
arbitrary starting point invariance principle may be derived from the invariance
principle of a single particle starting from the origin. Therefore, our hydrodynamics
result applies to the examples of quenched environments considered in, e.g., [1],
[3], [6] in combination with the hypothesis of uniform ellipticity.
acknowledgement: "We warmly thank S.R.S. Varadhan for many enlightening discussions
at an early stage of this work. We are indebted to Francesca Collet for fruitful
discussions and constant support all throughout this work. We thank Simone Floreani\r\nand
Alberto Chiarini for helpful conversations on the final part of this paper as well
as both referees for their careful reading and for raising relevant issues on some
weak points contained in a previous version of this manuscript; we believe this
helped us to improve it.\r\nPart of this work was done during the authors’ stay
at the Institut Henri Poincaré (UMS 5208 CNRS-Sorbonne Université) – Centre Emile
Borel during the trimester Stochastic Dynamics Out of Equilibrium. The authors thank
this institution for hospitality and support (through LabEx CARMIN, ANR-10-LABX-59-01).
F.S. thanks laboratoire\r\nMAP5 of Université de Paris, and E.S. thanks Delft University,
for financial support and hospitality. F.S. acknowledges NWO for financial support
via the TOP1 grant 613.001.552 as well as funding from the European Union’s Horizon
2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement
No. 754411. This research has been conducted within the FP2M federation (CNRS FR
2036)."
article_number: '138'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Frank
full_name: Redig, Frank
last_name: Redig
- first_name: Ellen
full_name: Saada, Ellen
last_name: Saada
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: 'Redig F, Saada E, Sau F. Symmetric simple exclusion process in dynamic environment:
Hydrodynamics. Electronic Journal of Probability. 2020;25. doi:10.1214/20-EJP536'
apa: 'Redig, F., Saada, E., & Sau, F. (2020). Symmetric simple exclusion process
in dynamic environment: Hydrodynamics. Electronic Journal of Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/20-EJP536'
chicago: 'Redig, Frank, Ellen Saada, and Federico Sau. “Symmetric Simple Exclusion
Process in Dynamic Environment: Hydrodynamics.” Electronic Journal of Probability. Institute
of Mathematical Statistics, 2020. https://doi.org/10.1214/20-EJP536.'
ieee: 'F. Redig, E. Saada, and F. Sau, “Symmetric simple exclusion process in dynamic
environment: Hydrodynamics,” Electronic Journal of Probability, vol. 25. Institute
of Mathematical Statistics, 2020.'
ista: 'Redig F, Saada E, Sau F. 2020. Symmetric simple exclusion process in dynamic
environment: Hydrodynamics. Electronic Journal of Probability. 25, 138.'
mla: 'Redig, Frank, et al. “Symmetric Simple Exclusion Process in Dynamic Environment:
Hydrodynamics.” Electronic Journal of Probability, vol. 25, 138, Institute
of Mathematical Statistics, 2020, doi:10.1214/20-EJP536.'
short: F. Redig, E. Saada, F. Sau, Electronic Journal of Probability 25 (2020).
date_created: 2020-12-27T23:01:17Z
date_published: 2020-10-21T00:00:00Z
date_updated: 2023-10-17T12:51:56Z
day: '21'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/20-EJP536
ec_funded: 1
external_id:
arxiv:
- '1811.01366'
isi:
- '000591737500001'
file:
- access_level: open_access
checksum: d75359b9814e78d57c0a481b7cde3751
content_type: application/pdf
creator: dernst
date_created: 2020-12-28T08:24:08Z
date_updated: 2020-12-28T08:24:08Z
file_id: '8976'
file_name: 2020_ElectronJProbab_Redig.pdf
file_size: 696653
relation: main_file
success: 1
file_date_updated: 2020-12-28T08:24:08Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Electronic Journal of Probability
publication_identifier:
eissn:
- 1083-6489
publication_status: published
publisher: ' Institute of Mathematical Statistics'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Symmetric simple exclusion process in dynamic environment: Hydrodynamics'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2020'
...
---
_id: '71'
abstract:
- lang: eng
text: "We consider dynamical transport metrics for probability measures on discretisations
of a bounded convex domain in ℝd. These metrics are natural discrete counterparts
to the Kantorovich metric \U0001D54E2, defined using a Benamou-Brenier type formula.
Under mild assumptions we prove an asymptotic upper bound for the discrete transport
metric Wt in terms of \U0001D54E2, as the size of the mesh T tends to 0. However,
we show that the corresponding lower bound may fail in general, even on certain
one-dimensional and symmetric two-dimensional meshes. In addition, we show that
the asymptotic lower bound holds under an isotropy assumption on the mesh, which
turns out to be essentially necessary. This assumption is satisfied, e.g., for
tilings by convex regular polygons, and it implies Gromov-Hausdorff convergence
of the transport metric."
article_processing_charge: No
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
citation:
ama: Gladbach P, Kopfer E, Maas J. Scaling limits of discrete optimal transport.
SIAM Journal on Mathematical Analysis. 2020;52(3):2759-2802. doi:10.1137/19M1243440
apa: Gladbach, P., Kopfer, E., & Maas, J. (2020). Scaling limits of discrete
optimal transport. SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/19M1243440
chicago: Gladbach, Peter, Eva Kopfer, and Jan Maas. “Scaling Limits of Discrete
Optimal Transport.” SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics, 2020. https://doi.org/10.1137/19M1243440.
ieee: P. Gladbach, E. Kopfer, and J. Maas, “Scaling limits of discrete optimal transport,”
SIAM Journal on Mathematical Analysis, vol. 52, no. 3. Society for Industrial
and Applied Mathematics, pp. 2759–2802, 2020.
ista: Gladbach P, Kopfer E, Maas J. 2020. Scaling limits of discrete optimal transport.
SIAM Journal on Mathematical Analysis. 52(3), 2759–2802.
mla: Gladbach, Peter, et al. “Scaling Limits of Discrete Optimal Transport.” SIAM
Journal on Mathematical Analysis, vol. 52, no. 3, Society for Industrial and
Applied Mathematics, 2020, pp. 2759–802, doi:10.1137/19M1243440.
short: P. Gladbach, E. Kopfer, J. Maas, SIAM Journal on Mathematical Analysis 52
(2020) 2759–2802.
date_created: 2018-12-11T11:44:28Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2023-09-18T08:13:15Z
day: '01'
department:
- _id: JaMa
doi: 10.1137/19M1243440
external_id:
arxiv:
- '1809.01092'
isi:
- '000546975100017'
intvolume: ' 52'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1809.01092
month: '10'
oa: 1
oa_version: Preprint
page: 2759-2802
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- '10957154'
issn:
- '00361410'
publication_status: published
publisher: Society for Industrial and Applied Mathematics
publist_id: '7983'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scaling limits of discrete optimal transport
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 52
year: '2020'
...
---
_id: '7388'
abstract:
- lang: eng
text: We give a Wong-Zakai type characterisation of the solutions of quasilinear
heat equations driven by space-time white noise in 1 + 1 dimensions. In order
to show that the renormalisation counterterms are local in the solution, a careful
arrangement of a few hundred terms is required. The main tool in this computation
is a general ‘integration by parts’ formula that provides a number of linear identities
for the renormalisation constants.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mate
full_name: Gerencser, Mate
id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
last_name: Gerencser
citation:
ama: Gerencser M. Nondivergence form quasilinear heat equations driven by space-time
white noise. Annales de l’Institut Henri Poincaré C, Analyse non linéaire.
2020;37(3):663-682. doi:10.1016/j.anihpc.2020.01.003
apa: Gerencser, M. (2020). Nondivergence form quasilinear heat equations driven
by space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse
Non Linéaire. Elsevier. https://doi.org/10.1016/j.anihpc.2020.01.003
chicago: Gerencser, Mate. “Nondivergence Form Quasilinear Heat Equations Driven
by Space-Time White Noise.” Annales de l’Institut Henri Poincaré C, Analyse
Non Linéaire. Elsevier, 2020. https://doi.org/10.1016/j.anihpc.2020.01.003.
ieee: M. Gerencser, “Nondivergence form quasilinear heat equations driven by space-time
white noise,” Annales de l’Institut Henri Poincaré C, Analyse non linéaire,
vol. 37, no. 3. Elsevier, pp. 663–682, 2020.
ista: Gerencser M. 2020. Nondivergence form quasilinear heat equations driven by
space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse non linéaire.
37(3), 663–682.
mla: Gerencser, Mate. “Nondivergence Form Quasilinear Heat Equations Driven by Space-Time
White Noise.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire,
vol. 37, no. 3, Elsevier, 2020, pp. 663–82, doi:10.1016/j.anihpc.2020.01.003.
short: M. Gerencser, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire
37 (2020) 663–682.
date_created: 2020-01-29T09:39:41Z
date_published: 2020-05-01T00:00:00Z
date_updated: 2023-08-17T14:35:46Z
day: '01'
department:
- _id: JaMa
doi: 10.1016/j.anihpc.2020.01.003
external_id:
arxiv:
- '1902.07635'
isi:
- '000531049800007'
intvolume: ' 37'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.07635
month: '05'
oa: 1
oa_version: Preprint
page: 663-682
publication: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
publication_identifier:
issn:
- 0294-1449
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nondivergence form quasilinear heat equations driven by space-time white noise
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 37
year: '2020'
...
---
_id: '74'
abstract:
- lang: eng
text: "We study the Gromov waist in the sense of t-neighborhoods for measures in
the Euclidean space, motivated by the famous theorem of Gromov about
\ the waist of radially symmetric Gaussian measures. In particular, it turns
our possible to extend Gromov’s original result to the case of not necessarily
\ radially symmetric Gaussian measure. We also provide examples of measures
having no t-neighborhood waist property, including a rather wide class\r\nof compactly
supported radially symmetric measures and their maps into the Euclidean space
of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument
\ to produce some estimates of t-neighborhoods of (weighted) volume-critical
submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic
manifolds in the complex projective space. In the appendix of this paper we provide
for reader’s convenience a more detailed explanation of the Caffarelli theorem
that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: 'Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial
non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional
Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1'
apa: Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian
measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.),
Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer
Nature. https://doi.org/10.1007/978-3-030-36020-7_1
chicago: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian
Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional
Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer
Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1.
ieee: A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures
and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis,
vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.
ista: 'Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures
and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis.
vol. 2256, 1–27.'
mla: Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian
Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional
Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer
Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.
short: A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects
of Functional Analysis, Springer Nature, 2020, pp. 1–27.
date_created: 2018-12-11T11:44:29Z
date_published: 2020-06-21T00:00:00Z
date_updated: 2023-08-17T13:48:31Z
day: '21'
department:
- _id: HeEd
- _id: JaMa
doi: 10.1007/978-3-030-36020-7_1
ec_funded: 1
editor:
- first_name: Bo'az
full_name: Klartag, Bo'az
last_name: Klartag
- first_name: Emanuel
full_name: Milman, Emanuel
last_name: Milman
external_id:
arxiv:
- '1808.07350'
isi:
- '000557689300003'
intvolume: ' 2256'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1808.07350
month: '06'
oa: 1
oa_version: Preprint
page: 1-27
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Geometric Aspects of Functional Analysis
publication_identifier:
eisbn:
- '9783030360207'
eissn:
- '16179692'
isbn:
- '9783030360191'
issn:
- '00758434'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNM
status: public
title: Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures
type: book_chapter
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2256
year: '2020'
...
---
_id: '7509'
abstract:
- lang: eng
text: "In this paper we study the joint convexity/concavity of the trace functions
Ψp,q,s(A,B)=Tr(Bq2K∗ApKBq2)s, p,q,s∈R,\r\nwhere A and B are positive definite
matrices and K is any fixed invertible matrix. We will give full range of (p,q,s)∈R3
for Ψp,q,s to be jointly convex/concave for all K. As a consequence, we confirm
a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture
of Audenaert and Datta and obtain the full range of (α,z) for α-z Rényi relative
entropies to be monotone under completely positive trace preserving maps. We also
give simpler proofs of many known results, including the concavity of Ψp,0,1/p
for 0Advances in Mathematics. 2020;365. doi:10.1016/j.aim.2020.107053
apa: Zhang, H. (2020). From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb
conjecture. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2020.107053
chicago: Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb
Conjecture.” Advances in Mathematics. Elsevier, 2020. https://doi.org/10.1016/j.aim.2020.107053.
ieee: H. Zhang, “From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture,”
Advances in Mathematics, vol. 365. Elsevier, 2020.
ista: Zhang H. 2020. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture.
Advances in Mathematics. 365, 107053.
mla: Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb Conjecture.”
Advances in Mathematics, vol. 365, 107053, Elsevier, 2020, doi:10.1016/j.aim.2020.107053.
short: H. Zhang, Advances in Mathematics 365 (2020).
date_created: 2020-02-23T21:43:50Z
date_published: 2020-05-13T00:00:00Z
date_updated: 2023-08-18T06:37:09Z
day: '13'
ddc:
- '515'
department:
- _id: JaMa
doi: 10.1016/j.aim.2020.107053
ec_funded: 1
external_id:
arxiv:
- '1811.01205'
isi:
- '000522798000001'
intvolume: ' 365'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1811.01205
month: '05'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Advances in Mathematics
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 365
year: '2020'
...