---
_id: '9230'
abstract:
- lang: eng
text: "We consider a model of the Riemann zeta function on the critical axis and
study its maximum over intervals of length (log T)θ, where θ is either fixed or
tends to zero at a suitable rate.\r\nIt is shown that the deterministic level
of the maximum interpolates smoothly between the ones\r\nof log-correlated variables
and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to
1/4’ in the second order. This provides a natural context where extreme value
statistics of\r\nlog-correlated variables with time-dependent variance and rate
occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate
for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian
correction. This correction is expected to be present for the\r\nRiemann zeta
function and pertains to the question of the correct order of the maximum of\r\nthe
zeta function in large intervals."
acknowledgement: The research of L.-P. A. is supported in part by the grant NSF CAREER
DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID
443891315 within SPP 2265 and Project-ID 446173099.
article_number: '2103.04817'
article_processing_charge: No
arxiv: 1
author:
- first_name: Louis-Pierre
full_name: Arguin, Louis-Pierre
last_name: Arguin
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
- first_name: Lisa
full_name: Hartung, Lisa
last_name: Hartung
citation:
ama: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta
function over intervals of varying length. arXiv. doi:10.48550/arXiv.2103.04817
apa: Arguin, L.-P., Dubach, G., & Hartung, L. (n.d.). Maxima of a random model
of the Riemann zeta function over intervals of varying length. arXiv. https://doi.org/10.48550/arXiv.2103.04817
chicago: Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a
Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv,
n.d. https://doi.org/10.48550/arXiv.2103.04817.
ieee: L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the
Riemann zeta function over intervals of varying length,” arXiv. .
ista: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta
function over intervals of varying length. arXiv, 2103.04817.
mla: Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta
Function over Intervals of Varying Length.” ArXiv, 2103.04817, doi:10.48550/arXiv.2103.04817.
short: L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).
date_created: 2021-03-09T11:08:15Z
date_published: 2021-03-08T00:00:00Z
date_updated: 2023-05-03T10:22:59Z
day: '08'
department:
- _id: LaEr
doi: 10.48550/arXiv.2103.04817
ec_funded: 1
external_id:
arxiv:
- '2103.04817'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.04817
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: arXiv
publication_status: submitted
status: public
title: Maxima of a random model of the Riemann zeta function over intervals of varying
length
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9281'
abstract:
- lang: eng
text: We comment on two formal proofs of Fermat's sum of two squares theorem, written
using the Mathematical Components libraries of the Coq proof assistant. The first
one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's
recent new proof relying on partition-theoretic arguments. Both formal proofs
rely on a general property of involutions of finite sets, of independent interest.
The proof technique consists for the most part of automating recurrent tasks (such
as case distinctions and computations on natural numbers) via ad hoc tactics.
article_number: '2103.11389'
article_processing_charge: No
arxiv: 1
author:
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
- first_name: Fabian
full_name: Mühlböck, Fabian
id: 6395C5F6-89DF-11E9-9C97-6BDFE5697425
last_name: Mühlböck
orcid: 0000-0003-1548-0177
citation:
ama: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv.
doi:10.48550/arXiv.2103.11389
apa: Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence
proof. arXiv. https://doi.org/10.48550/arXiv.2103.11389
chicago: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s
One-Sentence Proof.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.11389.
ieee: G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,”
arXiv. .
ista: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof.
arXiv, 2103.11389.
mla: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence
Proof.” ArXiv, 2103.11389, doi:10.48550/arXiv.2103.11389.
short: G. Dubach, F. Mühlböck, ArXiv (n.d.).
date_created: 2021-03-23T05:38:48Z
date_published: 2021-03-21T00:00:00Z
date_updated: 2023-05-03T10:26:45Z
day: '21'
department:
- _id: LaEr
- _id: ToHe
doi: 10.48550/arXiv.2103.11389
ec_funded: 1
external_id:
arxiv:
- '2103.11389'
language:
- iso: eng
main_file_link:
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url: https://arxiv.org/abs/2103.11389
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oa: 1
oa_version: Preprint
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call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '9946'
relation: other
status: public
status: public
title: Formal verification of Zagier's one-sentence proof
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9412'
abstract:
- lang: eng
text: We extend our recent result [22] on the central limit theorem for the linear
eigenvalue statistics of non-Hermitian matrices X with independent, identically
distributed complex entries to the real symmetry class. We find that the expectation
and variance substantially differ from their complex counterparts, reflecting
(i) the special spectral symmetry of real matrices onto the real axis; and (ii)
the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes
the previously known special cases where either the test function is analytic
[49] or the first four moments of the matrix elements match the real Gaussian
[59, 44]. The key element of the proof is the analysis of several weakly dependent
Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared
with [22] is that the correlation structure of the stochastic differentials in
each individual DBM is non-trivial, potentially even jeopardising its well-posedness.
article_number: '24'
article_processing_charge: No
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Fluctuation around the circular law for
random matrices with real entries. Electronic Journal of Probability. 2021;26.
doi:10.1214/21-EJP591
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Fluctuation around
the circular law for random matrices with real entries. Electronic Journal
of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP591
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation
around the Circular Law for Random Matrices with Real Entries.” Electronic
Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP591.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular
law for random matrices with real entries,” Electronic Journal of Probability,
vol. 26. Institute of Mathematical Statistics, 2021.
ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Fluctuation around the circular law
for random matrices with real entries. Electronic Journal of Probability. 26,
24.
mla: Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random
Matrices with Real Entries.” Electronic Journal of Probability, vol. 26,
24, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP591.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability
26 (2021).
date_created: 2021-05-23T22:01:44Z
date_published: 2021-03-23T00:00:00Z
date_updated: 2023-08-08T13:39:19Z
day: '23'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/21-EJP591
ec_funded: 1
external_id:
arxiv:
- '2002.02438'
isi:
- '000641855600001'
file:
- access_level: open_access
checksum: 864ab003ad4cffea783f65aa8c2ba69f
content_type: application/pdf
creator: kschuh
date_created: 2021-05-25T13:24:19Z
date_updated: 2021-05-25T13:24:19Z
file_id: '9423'
file_name: 2021_EJP_Cipolloni.pdf
file_size: 865148
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file_date_updated: 2021-05-25T13:24:19Z
has_accepted_license: '1'
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isi: 1
language:
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month: '03'
oa: 1
oa_version: Published Version
project:
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call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Electronic Journal of Probability
publication_identifier:
eissn:
- '10836489'
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fluctuation around the circular law for random matrices with real entries
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)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 26
year: '2021'
...
---
_id: '9550'
abstract:
- lang: eng
text: 'We prove that the energy of any eigenvector of a sum of several independent
large Wigner matrices is equally distributed among these matrices with very high
precision. This shows a particularly strong microcanonical form of the equipartition
principle for quantum systems whose components are modelled by Wigner matrices. '
acknowledgement: The first author is supported in part by Hong Kong RGC Grant GRF
16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced
Grant RANMAT 338804. The third author is supported in part by Swedish Research Council
Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation
article_number: e44
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum
of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38
apa: Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for
Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press.
https://doi.org/10.1017/fms.2021.38
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle
for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University
Press, 2021. https://doi.org/10.1017/fms.2021.38.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,”
Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021.
ista: Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices.
Forum of Mathematics, Sigma. 9, e44.
mla: Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” Forum
of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38.
short: Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).
date_created: 2021-06-13T22:01:33Z
date_published: 2021-05-27T00:00:00Z
date_updated: 2023-08-08T14:03:40Z
day: '27'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2021.38
ec_funded: 1
external_id:
arxiv:
- '2008.07061'
isi:
- '000654960800001'
file:
- access_level: open_access
checksum: 47c986578de132200d41e6d391905519
content_type: application/pdf
creator: cziletti
date_created: 2021-06-15T14:40:45Z
date_updated: 2021-06-15T14:40:45Z
file_id: '9555'
file_name: 2021_ForumMath_Bao.pdf
file_size: 483458
relation: main_file
success: 1
file_date_updated: 2021-06-15T14:40:45Z
has_accepted_license: '1'
intvolume: ' 9'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- '20505094'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equipartition principle for Wigner matrices
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: 9
year: '2021'
...
---
_id: '10221'
abstract:
- lang: eng
text: We prove that any deterministic matrix is approximately the identity in the
eigenbasis of a large random Wigner matrix with very high probability and with
an optimal error inversely proportional to the square root of the dimension. Our
theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch
(Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner
ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity
(QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing
previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278,
2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for
Wigner matrices. Communications in Mathematical Physics. 2021;388(2):1005–1048.
doi:10.1007/s00220-021-04239-z
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Eigenstate thermalization
hypothesis for Wigner matrices. Communications in Mathematical Physics.
Springer Nature. https://doi.org/10.1007/s00220-021-04239-z
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization
Hypothesis for Wigner Matrices.” Communications in Mathematical Physics.
Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04239-z.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis
for Wigner matrices,” Communications in Mathematical Physics, vol. 388,
no. 2. Springer Nature, pp. 1005–1048, 2021.
ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis
for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.
mla: Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner
Matrices.” Communications in Mathematical Physics, vol. 388, no. 2, Springer
Nature, 2021, pp. 1005–1048, doi:10.1007/s00220-021-04239-z.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics
388 (2021) 1005–1048.
date_created: 2021-11-07T23:01:25Z
date_published: 2021-10-29T00:00:00Z
date_updated: 2023-08-14T10:29:49Z
day: '29'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-021-04239-z
external_id:
arxiv:
- '2012.13215'
isi:
- '000712232700001'
file:
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date_created: 2022-02-02T10:19:55Z
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file_name: 2021_CommunMathPhys_Cipolloni.pdf
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oa_version: Published Version
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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: Eigenstate thermalization hypothesis for Wigner matrices
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: 388
year: '2021'
...
---
_id: '10285'
abstract:
- lang: eng
text: We study the overlaps between right and left eigenvectors for random matrices
of the spherical ensemble, as well as truncated unitary ensembles in the regime
where half of the matrix at least is truncated. These two integrable models exhibit
a form of duality, and the essential steps of our investigation can therefore
be performed in parallel. In every case, conditionally on all eigenvalues, diagonal
overlaps are shown to be distributed as a product of independent random variables
with explicit distributions. This enables us to prove that the scaled diagonal
overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail
limit, namely, the inverse of a γ2 distribution. We also provide formulae for
the conditional expectation of diagonal and off-diagonal overlaps, either with
respect to one eigenvalue, or with respect to the whole spectrum. These results,
analogous to what is known for the complex Ginibre ensemble, can be obtained in
these cases thanks to integration techniques inspired from a previous work by
Forrester & Krishnapur.
acknowledgement: We acknowledge partial support from the grants NSF DMS-1812114 of
P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has
also received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would
like to thank Paul Bourgade and László Erdős for many helpful comments.
article_number: '124'
article_processing_charge: No
article_type: original
author:
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
citation:
ama: Dubach G. On eigenvector statistics in the spherical and truncated unitary
ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686
apa: Dubach, G. (2021). On eigenvector statistics in the spherical and truncated
unitary ensembles. Electronic Journal of Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/21-EJP686
chicago: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated
Unitary Ensembles.” Electronic Journal of Probability. Institute of Mathematical
Statistics, 2021. https://doi.org/10.1214/21-EJP686.
ieee: G. Dubach, “On eigenvector statistics in the spherical and truncated unitary
ensembles,” Electronic Journal of Probability, vol. 26. Institute of Mathematical
Statistics, 2021.
ista: Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary
ensembles. Electronic Journal of Probability. 26, 124.
mla: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated
Unitary Ensembles.” Electronic Journal of Probability, vol. 26, 124, Institute
of Mathematical Statistics, 2021, doi:10.1214/21-EJP686.
short: G. Dubach, Electronic Journal of Probability 26 (2021).
date_created: 2021-11-14T23:01:25Z
date_published: 2021-09-28T00:00:00Z
date_updated: 2021-11-15T10:48:46Z
day: '28'
ddc:
- '519'
department:
- _id: LaEr
doi: 10.1214/21-EJP686
ec_funded: 1
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language:
- iso: eng
month: '09'
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: On eigenvector statistics in the spherical and truncated unitary ensembles
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 26
year: '2021'
...
---
_id: '9912'
abstract:
- lang: eng
text: "In the customary random matrix model for transport in quantum dots with M
internal degrees of freedom coupled to a chaotic environment via \U0001D441≪\U0001D440
channels, the density \U0001D70C of transmission eigenvalues is computed from
a specific invariant ensemble for which explicit formula for the joint probability
density of all eigenvalues is available. We revisit this problem in the large
N regime allowing for (i) arbitrary ratio \U0001D719:=\U0001D441/\U0001D440≤1;
and (ii) general distributions for the matrix elements of the Hamiltonian of the
quantum dot. In the limit \U0001D719→0, we recover the formula for the density
\U0001D70C that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special
matrix ensemble. We also prove that the inverse square root singularity of the
density at zero and full transmission in Beenakker’s formula persists for any
\U0001D719<1 but in the borderline case \U0001D719=1 an anomalous \U0001D706−2/3
singularity arises at zero. To access this level of generality, we develop the
theory of global and local laws on the spectral density of a large class of noncommutative
rational expressions in large random matrices with i.i.d. entries."
acknowledgement: The authors are very grateful to Yan Fyodorov for discussions on
the physical background and for providing references, and to the anonymous referee
for numerous valuable remarks.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative
rational functions. Annales Henri Poincaré . 2021;22:4205–4269. doi:10.1007/s00023-021-01085-6
apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2021). Scattering in quantum dots
via noncommutative rational functions. Annales Henri Poincaré . Springer
Nature. https://doi.org/10.1007/s00023-021-01085-6
chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum
Dots via Noncommutative Rational Functions.” Annales Henri Poincaré . Springer
Nature, 2021. https://doi.org/10.1007/s00023-021-01085-6.
ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative
rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature,
pp. 4205–4269, 2021.
ista: Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative
rational functions. Annales Henri Poincaré . 22, 4205–4269.
mla: Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational
Functions.” Annales Henri Poincaré , vol. 22, Springer Nature, 2021, pp.
4205–4269, doi:10.1007/s00023-021-01085-6.
short: L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.
date_created: 2021-08-15T22:01:29Z
date_published: 2021-12-01T00:00:00Z
date_updated: 2023-08-11T10:31:48Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-021-01085-6
ec_funded: 1
external_id:
arxiv:
- '1911.05112'
isi:
- '000681531500001'
file:
- access_level: open_access
checksum: 8d6bac0e2b0a28539608b0538a8e3b38
content_type: application/pdf
creator: dernst
date_created: 2022-05-12T12:50:27Z
date_updated: 2022-05-12T12:50:27Z
file_id: '11365'
file_name: 2021_AnnHenriPoincare_Erdoes.pdf
file_size: 1162454
relation: main_file
success: 1
file_date_updated: 2022-05-12T12:50:27Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 4205–4269
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: 'Annales Henri Poincaré '
publication_identifier:
eissn:
- 1424-0661
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scattering in quantum dots via noncommutative rational functions
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: 22
year: '2021'
...
---
_id: '10862'
abstract:
- lang: eng
text: We consider the sum of two large Hermitian matrices A and B with a Haar unitary
conjugation bringing them into a general relative position. We prove that the
eigenvalue density on the scale slightly above the local eigenvalue spacing is
asymptotically given by the free additive convolution of the laws of A and B as
the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues
and optimal rate of convergence in Voiculescu's theorem. Our previous works [4],
[5] established these results in the bulk spectrum, the current paper completely
settles the problem at the spectral edges provided they have the typical square-root
behavior. The key element of our proof is to compensate the deterioration of the
stability of the subordination equations by sharp error estimates that properly
account for the local density near the edge. Our results also hold if the Haar
unitary matrix is replaced by the Haar orthogonal matrix.
acknowledgement: Partially supported by ERC Advanced Grant RANMAT No. 338804.
article_number: '108639'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Kevin
full_name: Schnelli, Kevin
last_name: Schnelli
citation:
ama: Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices
at the regular edge. Journal of Functional Analysis. 2020;279(7). doi:10.1016/j.jfa.2020.108639
apa: Bao, Z., Erdös, L., & Schnelli, K. (2020). Spectral rigidity for addition
of random matrices at the regular edge. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2020.108639
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for
Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis.
Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108639.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random
matrices at the regular edge,” Journal of Functional Analysis, vol. 279,
no. 7. Elsevier, 2020.
ista: Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random
matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.
mla: Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at
the Regular Edge.” Journal of Functional Analysis, vol. 279, no. 7, 108639,
Elsevier, 2020, doi:10.1016/j.jfa.2020.108639.
short: Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).
date_created: 2022-03-18T10:18:59Z
date_published: 2020-10-15T00:00:00Z
date_updated: 2023-08-24T14:08:42Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2020.108639
ec_funded: 1
external_id:
arxiv:
- '1708.01597'
isi:
- '000559623200009'
intvolume: ' 279'
isi: 1
issue: '7'
keyword:
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.01597
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral rigidity for addition of random matrices at the regular edge
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 279
year: '2020'
...
---
_id: '7389'
abstract:
- lang: eng
text: "Recently Kloeckner described the structure of the isometry group of the quadratic
Wasserstein space W_2(R^n). It turned out that the case of the real line is exceptional
in the sense that there exists an exotic isometry flow. Following this line of
investigation, we compute Isom(W_p(R)), the isometry group of the Wasserstein
space\r\nW_p(R) for all p \\in [1,\\infty) \\setminus {2}. We show that W_2(R)
is also exceptional regarding the\r\nparameter p: W_p(R) is isometrically rigid
if and only if p is not equal to 2. Regarding the underlying\r\nspace, we prove
that the exceptionality of p = 2 disappears if we replace R by the compact\r\ninterval
[0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only
if\r\np is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass,
and Isom(W_1([0,1]))\r\ncannot be embedded into Isom(W_1(R))."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gyorgy Pal
full_name: Geher, Gyorgy Pal
last_name: Geher
- first_name: Tamas
full_name: Titkos, Tamas
last_name: Titkos
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the
real line. Transactions of the American Mathematical Society. 2020;373(8):5855-5883.
doi:10.1090/tran/8113
apa: Geher, G. P., Titkos, T., & Virosztek, D. (2020). Isometric study of Wasserstein
spaces - the real line. Transactions of the American Mathematical Society.
American Mathematical Society. https://doi.org/10.1090/tran/8113
chicago: Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study
of Wasserstein Spaces - the Real Line.” Transactions of the American Mathematical
Society. American Mathematical Society, 2020. https://doi.org/10.1090/tran/8113.
ieee: G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein
spaces - the real line,” Transactions of the American Mathematical Society,
vol. 373, no. 8. American Mathematical Society, pp. 5855–5883, 2020.
ista: Geher GP, Titkos T, Virosztek D. 2020. Isometric study of Wasserstein spaces
- the real line. Transactions of the American Mathematical Society. 373(8), 5855–5883.
mla: Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real
Line.” Transactions of the American Mathematical Society, vol. 373, no.
8, American Mathematical Society, 2020, pp. 5855–83, doi:10.1090/tran/8113.
short: G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical
Society 373 (2020) 5855–5883.
date_created: 2020-01-29T10:20:46Z
date_published: 2020-08-01T00:00:00Z
date_updated: 2023-08-17T14:31:03Z
day: '01'
ddc:
- '515'
department:
- _id: LaEr
doi: 10.1090/tran/8113
ec_funded: 1
external_id:
arxiv:
- '2002.00859'
isi:
- '000551418100018'
intvolume: ' 373'
isi: 1
issue: '8'
keyword:
- Wasserstein space
- isometric embeddings
- isometric rigidity
- exotic isometry flow
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2002.00859
month: '08'
oa: 1
oa_version: Preprint
page: 5855-5883
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '846294'
name: Geometric study of Wasserstein spaces and free probability
publication: Transactions of the American Mathematical Society
publication_identifier:
eissn:
- '10886850'
issn:
- '00029947'
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: Isometric study of Wasserstein spaces - the real line
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 373
year: '2020'
...
---
_id: '7512'
abstract:
- lang: eng
text: We consider general self-adjoint polynomials in several independent random
matrices whose entries are centered and have the same variance. We show that under
certain conditions the local law holds up to the optimal scale, i.e., the eigenvalue
density on scales just above the eigenvalue spacing follows the global density
of states which is determined by free probability theory. We prove that these
conditions hold for general homogeneous polynomials of degree two and for symmetrized
products of independent matrices with i.i.d. entries, thus establishing the optimal
bulk local law for these classes of ensembles. In particular, we generalize a
similar result of Anderson for anticommutator. For more general polynomials our
conditions are effectively checkable numerically.
acknowledgement: "The authors are grateful to Oskari Ajanki for his invaluable help
at the initial stage of this project, to Serban Belinschi for useful discussions,
to Alexander Tikhomirov for calling our attention to the model example in Section
6.2 and to the anonymous referee for suggesting to simplify certain proofs. Erdös:
Partially funded by ERC Advanced Grant RANMAT No. 338804\r\n"
article_number: '108507'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices.
Journal of Functional Analysis. 2020;278(12). doi:10.1016/j.jfa.2020.108507
apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2020). Local laws for polynomials
of Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108507
chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials
of Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108507.
ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner
matrices,” Journal of Functional Analysis, vol. 278, no. 12. Elsevier,
2020.
ista: Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices.
Journal of Functional Analysis. 278(12), 108507.
mla: Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” Journal
of Functional Analysis, vol. 278, no. 12, 108507, Elsevier, 2020, doi:10.1016/j.jfa.2020.108507.
short: L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).
date_created: 2020-02-23T23:00:36Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2023-08-18T06:36:10Z
day: '01'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2020.108507
ec_funded: 1
external_id:
arxiv:
- '1804.11340'
isi:
- '000522798900001'
intvolume: ' 278'
isi: 1
issue: '12'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.11340
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- '10960783'
issn:
- '00221236'
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local laws for polynomials of Wigner matrices
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 278
year: '2020'
...
---
_id: '7618'
abstract:
- lang: eng
text: 'This short note aims to study quantum Hellinger distances investigated recently
by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis
on barycenters. We introduce the family of generalized quantum Hellinger divergences
that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando
mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to
the family of maximal quantum f-divergences, and hence are jointly convex, and
satisfy the data processing inequality. We derive a characterization of the barycenter
of finitely many positive definite operators for these generalized quantum Hellinger
divergences. We note that the characterization of the barycenter as the weighted
multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true
in the case of commuting operators, but it is not correct in the general case. '
acknowledgement: "J. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum
Grant for Quantum\r\nInformation Theory, No. 96 141, and by the Hungarian National
Research, Development and Innovation\r\nOffice (NKFIH) via Grants Nos. K119442,
K124152 and KH129601. D. Virosztek was supported by the\r\nISTFELLOW program of
the Institute of Science and Technology Austria (Project Code IC1027FELL01),\r\nby
the European Union’s Horizon 2020 research and innovation program under the Marie\r\nSklodowska-Curie
Grant Agreement No. 846294, and partially supported by the Hungarian National\r\nResearch,
Development and Innovation Office (NKFIH) via Grants Nos. K124152 and KH129601.\r\nWe
are grateful to Milán Mosonyi for drawing our attention to Ref.’s [6,14,15,17,\r\n20,21],
for comments on earlier versions of this paper, and for several discussions on the
topic. We are\r\nalso grateful to Miklós Pálfia for several discussions; to László
Erdös for his essential suggestions on the\r\nstructure and highlights of this paper,
and for his comments on earlier versions; and to the anonymous\r\nreferee for his/her
valuable comments and suggestions."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jozsef
full_name: Pitrik, Jozsef
last_name: Pitrik
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Pitrik J, Virosztek D. Quantum Hellinger distances revisited. Letters in
Mathematical Physics. 2020;110(8):2039-2052. doi:10.1007/s11005-020-01282-0
apa: Pitrik, J., & Virosztek, D. (2020). Quantum Hellinger distances revisited.
Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-020-01282-0
chicago: Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.”
Letters in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s11005-020-01282-0.
ieee: J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” Letters
in Mathematical Physics, vol. 110, no. 8. Springer Nature, pp. 2039–2052,
2020.
ista: Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters
in Mathematical Physics. 110(8), 2039–2052.
mla: Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.”
Letters in Mathematical Physics, vol. 110, no. 8, Springer Nature, 2020,
pp. 2039–52, doi:10.1007/s11005-020-01282-0.
short: J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052.
date_created: 2020-03-25T15:57:48Z
date_published: 2020-08-01T00:00:00Z
date_updated: 2023-08-18T10:17:26Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s11005-020-01282-0
ec_funded: 1
external_id:
arxiv:
- '1903.10455'
isi:
- '000551556000002'
intvolume: ' 110'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1903.10455
month: '08'
oa: 1
oa_version: Preprint
page: 2039-2052
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '846294'
name: Geometric study of Wasserstein spaces and free probability
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Letters in Mathematical Physics
publication_identifier:
eissn:
- 1573-0530
issn:
- 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantum Hellinger distances revisited
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 110
year: '2020'
...
---
_id: '6184'
abstract:
- lang: eng
text: We prove edge universality for a general class of correlated real symmetric
or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also
applies to internal edges of the self-consistent density of states. In particular,
we establish a strong form of band rigidity which excludes mismatches between
location and label of eigenvalues close to internal edges in these general models.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: 'Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity
and edge universality. Annals of Probability. 2020;48(2):963-1001. doi:10.1214/19-AOP1379'
apa: 'Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Correlated
random matrices: Band rigidity and edge universality. Annals of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/19-AOP1379'
chicago: 'Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder.
“Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of
Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/19-AOP1379.'
ieee: 'J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices:
Band rigidity and edge universality,” Annals of Probability, vol. 48, no.
2. Institute of Mathematical Statistics, pp. 963–1001, 2020.'
ista: 'Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices:
Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.'
mla: 'Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge
Universality.” Annals of Probability, vol. 48, no. 2, Institute of Mathematical
Statistics, 2020, pp. 963–1001, doi:10.1214/19-AOP1379.'
short: J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020)
963–1001.
date_created: 2019-03-28T09:20:08Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2024-02-22T14:34:33Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/19-AOP1379
ec_funded: 1
external_id:
arxiv:
- '1804.07744'
isi:
- '000528269100013'
intvolume: ' 48'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.07744
month: '03'
oa: 1
oa_version: Preprint
page: 963-1001
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Annals of Probability
publication_identifier:
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: 'Correlated random matrices: Band rigidity and edge universality'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2020'
...
---
_id: '6185'
abstract:
- lang: eng
text: For complex Wigner-type matrices, i.e. Hermitian random matrices with independent,
not necessarily identically distributed entries above the diagonal, we show that
at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue
statistics are universal and form a Pearcey process. Since the density of states
typically exhibits only square root or cubic root cusp singularities, our work
complements previous results on the bulk and edge universality and it thus completes
the resolution of the Wigner–Dyson–Mehta universality conjecture for the last
remaining universality type in the complex Hermitian class. Our analysis holds
not only for exact cusps, but approximate cusps as well, where an extended Pearcey
process emerges. As a main technical ingredient we prove an optimal local law
at the cusp for both symmetry classes. This result is also the key input in the
companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where
the cusp universality for real symmetric Wigner-type matrices is proven. The novel
cusp fluctuation mechanism is also essential for the recent results on the spectral
radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random
matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian
edge universality (Cipolloni et al. in Edge universality for non-Hermitian random
matrices, 2019. arXiv:1908.00969).
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). The authors are very grateful to Johannes Alt for numerous discussions
on the Dyson equation and for his invaluable help in adjusting [10] to the needs
of the present work.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: 'Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I:
Local law and the complex Hermitian case. Communications in Mathematical Physics.
2020;378:1203-1278. doi:10.1007/s00220-019-03657-4'
apa: 'Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Cusp universality
for random matrices I: Local law and the complex Hermitian case. Communications
in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03657-4'
chicago: 'Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality
for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications
in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03657-4.'
ieee: 'L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random
matrices I: Local law and the complex Hermitian case,” Communications in Mathematical
Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.'
ista: 'Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices
I: Local law and the complex Hermitian case. Communications in Mathematical Physics.
378, 1203–1278.'
mla: 'Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law
and the Complex Hermitian Case.” Communications in Mathematical Physics,
vol. 378, Springer Nature, 2020, pp. 1203–78, doi:10.1007/s00220-019-03657-4.'
short: L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics
378 (2020) 1203–1278.
date_created: 2019-03-28T10:21:15Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2023-09-07T12:54:12Z
day: '01'
ddc:
- '530'
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-019-03657-4
ec_funded: 1
external_id:
arxiv:
- '1809.03971'
isi:
- '000529483000001'
file:
- access_level: open_access
checksum: c3a683e2afdcea27afa6880b01e53dc2
content_type: application/pdf
creator: dernst
date_created: 2020-11-18T11:14:37Z
date_updated: 2020-11-18T11:14:37Z
file_id: '8771'
file_name: 2020_CommMathPhysics_Erdoes.pdf
file_size: 2904574
relation: main_file
success: 1
file_date_updated: 2020-11-18T11:14:37Z
has_accepted_license: '1'
intvolume: ' 378'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1203-1278
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: 'Cusp universality for random matrices I: Local law and the complex Hermitian
case'
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: 378
year: '2020'
...
---
_id: '6488'
abstract:
- lang: eng
text: We prove a central limit theorem for the difference of linear eigenvalue statistics
of a sample covariance matrix W˜ and its minor W. We find that the fluctuation
of this difference is much smaller than those of the individual linear statistics,
as a consequence of the strong correlation between the eigenvalues of W˜ and W.
Our result identifies the fluctuation of the spatial derivative of the approximate
Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar
result for Wigner matrices, for sample covariance matrices, the fluctuation may
entirely vanish.
article_number: '2050006'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: 'Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics
for sample covariance matrices. Random Matrices: Theory and Application.
2020;9(3). doi:10.1142/S2010326320500069'
apa: 'Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear
eigenvalue statistics for sample covariance matrices. Random Matrices: Theory
and Application. World Scientific Publishing. https://doi.org/10.1142/S2010326320500069'
chicago: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of
Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices:
Theory and Application. World Scientific Publishing, 2020. https://doi.org/10.1142/S2010326320500069.'
ieee: 'G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue
statistics for sample covariance matrices,” Random Matrices: Theory and Application,
vol. 9, no. 3. World Scientific Publishing, 2020.'
ista: 'Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue
statistics for sample covariance matrices. Random Matrices: Theory and Application.
9(3), 2050006.'
mla: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear
Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory
and Application, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020,
doi:10.1142/S2010326320500069.'
short: 'G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).'
date_created: 2019-05-26T21:59:14Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2023-08-28T08:38:48Z
day: '01'
department:
- _id: LaEr
doi: 10.1142/S2010326320500069
ec_funded: 1
external_id:
arxiv:
- '1806.08751'
isi:
- '000547464400001'
intvolume: ' 9'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1806.08751
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: 'Random Matrices: Theory and Application'
publication_identifier:
eissn:
- '20103271'
issn:
- '20103263'
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fluctuations for differences of linear eigenvalue statistics for sample covariance
matrices
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 9
year: '2020'
...
---
_id: '14694'
abstract:
- lang: eng
text: We study the unique solution m of the Dyson equation \( -m(z)^{-1} = z\1 -
a + S[m(z)] \) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies
in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving
linear operator on A. We show that m is the Stieltjes transform of a compactly
supported A-valued measure on R. Under suitable assumptions, we establish that
this measure has a uniformly 1/3-Hölder continuous density with respect to the
Lebesgue measure, which is supported on finitely many intervals, called bands.
In fact, the density is analytic inside the bands with a square-root growth at
the edges and internal cubic root cusps whenever the gap between two bands vanishes.
The shape of these singularities is universal and no other singularity may occur.
We give a precise asymptotic description of m near the singular points. These
asymptotics generalize the analysis at the regular edges given in the companion
paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated
random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020;
Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality
at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1,
No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math.
Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite
dimensional band mass formula from [the first author et al., loc. cit.] to the
von Neumann algebra setting by showing that the spectral mass of the bands is
topologically rigid under deformations and we conclude that these masses are quantized
in some important cases.
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: 'Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral
bands, edges and cusps. Documenta Mathematica. 2020;25:1421-1539. doi:10.4171/dm/780'
apa: 'Alt, J., Erdös, L., & Krüger, T. H. (2020). The Dyson equation with linear
self-energy: Spectral bands, edges and cusps. Documenta Mathematica. EMS
Press. https://doi.org/10.4171/dm/780'
chicago: 'Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation
with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica.
EMS Press, 2020. https://doi.org/10.4171/dm/780.'
ieee: 'J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy:
Spectral bands, edges and cusps,” Documenta Mathematica, vol. 25. EMS Press,
pp. 1421–1539, 2020.'
ista: 'Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy:
Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539.'
mla: 'Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral
Bands, Edges and Cusps.” Documenta Mathematica, vol. 25, EMS Press, 2020,
pp. 1421–539, doi:10.4171/dm/780.'
short: J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539.
date_created: 2023-12-18T10:37:43Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2023-12-18T10:46:09Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.4171/dm/780
external_id:
arxiv:
- '1804.07752'
file:
- access_level: open_access
checksum: 12aacc1d63b852ff9a51c1f6b218d4a6
content_type: application/pdf
creator: dernst
date_created: 2023-12-18T10:42:32Z
date_updated: 2023-12-18T10:42:32Z
file_id: '14695'
file_name: 2020_DocumentaMathematica_Alt.pdf
file_size: 1374708
relation: main_file
success: 1
file_date_updated: 2023-12-18T10:42:32Z
has_accepted_license: '1'
intvolume: ' 25'
keyword:
- General Mathematics
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1421-1539
publication: Documenta Mathematica
publication_identifier:
eissn:
- 1431-0643
issn:
- 1431-0635
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
record:
- id: '6183'
relation: earlier_version
status: public
status: public
title: 'The Dyson equation with linear self-energy: Spectral bands, edges and cusps'
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: 25
year: '2020'
...
---
_id: '15063'
abstract:
- lang: eng
text: We consider the least singular value of a large random matrix with real or
complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal
lower tail estimate on this singular value in the critical regime where z is around
the spectral edge, thus improving the classical bound of Sankar, Spielman and
Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation
in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on
the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395).
acknowledgement: Partially supported by ERC Advanced Grant No. 338804. This project
has received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Sklodowska-Curie Grant Agreement No. 66538
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular
value of the shifted Ginibre ensemble. Probability and Mathematical Physics.
2020;1(1):101-146. doi:10.2140/pmp.2020.1.101
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2020). Optimal lower bound
on the least singular value of the shifted Ginibre ensemble. Probability and
Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2020.1.101
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower
Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” Probability
and Mathematical Physics. Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/pmp.2020.1.101.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least
singular value of the shifted Ginibre ensemble,” Probability and Mathematical
Physics, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.
ista: Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least
singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics.
1(1), 101–146.
mla: Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value
of the Shifted Ginibre Ensemble.” Probability and Mathematical Physics,
vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:10.2140/pmp.2020.1.101.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics
1 (2020) 101–146.
date_created: 2024-03-04T10:27:57Z
date_published: 2020-11-16T00:00:00Z
date_updated: 2024-03-04T10:33:15Z
day: '16'
department:
- _id: LaEr
doi: 10.2140/pmp.2020.1.101
ec_funded: 1
external_id:
arxiv:
- '1908.01653'
intvolume: ' 1'
issue: '1'
keyword:
- General Medicine
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1908.01653
month: '11'
oa: 1
oa_version: Preprint
page: 101-146
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Probability and Mathematical Physics
publication_identifier:
issn:
- 2690-1005
- 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal lower bound on the least singular value of the shifted Ginibre ensemble
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2020'
...
---
_id: '9104'
abstract:
- lang: eng
text: We consider the free additive convolution of two probability measures μ and
ν on the real line and show that μ ⊞ v is supported on a single interval if μ
and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven
to vanish as a square root near the edges of its support if both μ and ν have
power law behavior with exponents between −1 and 1 near their edges. In particular,
these results show the ubiquity of the conditions in our recent work on optimal
local law at the spectral edges for addition of random matrices [5].
acknowledgement: "Supported in part by Hong Kong RGC Grant ECS 26301517.\r\nSupported
in part by ERC Advanced Grant RANMAT No. 338804.\r\nSupported in part by the Knut
and Alice Wallenberg Foundation and the Swedish Research Council Grant VR-2017-05195."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Bao Z, Erdös L, Schnelli K. On the support of the free additive convolution.
Journal d’Analyse Mathematique. 2020;142:323-348. doi:10.1007/s11854-020-0135-2
apa: Bao, Z., Erdös, L., & Schnelli, K. (2020). On the support of the free additive
convolution. Journal d’Analyse Mathematique. Springer Nature. https://doi.org/10.1007/s11854-020-0135-2
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the
Free Additive Convolution.” Journal d’Analyse Mathematique. Springer Nature,
2020. https://doi.org/10.1007/s11854-020-0135-2.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,”
Journal d’Analyse Mathematique, vol. 142. Springer Nature, pp. 323–348,
2020.
ista: Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution.
Journal d’Analyse Mathematique. 142, 323–348.
mla: Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” Journal
d’Analyse Mathematique, vol. 142, Springer Nature, 2020, pp. 323–48, doi:10.1007/s11854-020-0135-2.
short: Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020)
323–348.
date_created: 2021-02-07T23:01:15Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2023-08-24T11:16:03Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s11854-020-0135-2
ec_funded: 1
external_id:
arxiv:
- '1804.11199'
isi:
- '000611879400008'
intvolume: ' 142'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.11199
month: '11'
oa: 1
oa_version: Preprint
page: 323-348
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Journal d'Analyse Mathematique
publication_identifier:
eissn:
- '15658538'
issn:
- '00217670'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the support of the free additive convolution
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 142
year: '2020'
...
---
_id: '10879'
abstract:
- lang: eng
text: We study effects of a bounded and compactly supported perturbation on multidimensional
continuum random Schrödinger operators in the region of complete localisation.
Our main emphasis is on Anderson orthogonality for random Schrödinger operators.
Among others, we prove that Anderson orthogonality does occur for Fermi energies
in the region of complete localisation with a non-zero probability. This partially
confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015),
560–565]. The spectral shift function plays an important role in our analysis
of Anderson orthogonality. We identify it with the index of the corresponding
pair of spectral projections and explore the consequences thereof. All our results
rely on the main technical estimate of this paper which guarantees separate exponential
decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b.
Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication
operator corresponding to the indicator function of a unit cube centred about
a∈Rd, and f is in a suitable class of functions of bounded variation with distributional
derivative supported in the region of complete localisation for H.
acknowledgement: M.G. was supported by the DFG under grant GE 2871/1-1.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Adrian M
full_name: Dietlein, Adrian M
id: 317CB464-F248-11E8-B48F-1D18A9856A87
last_name: Dietlein
- first_name: Martin
full_name: Gebert, Martin
last_name: Gebert
- first_name: Peter
full_name: Müller, Peter
last_name: Müller
citation:
ama: Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger
operators with applications to Anderson orthogonality and the spectral shift function.
Journal of Spectral Theory. 2019;9(3):921-965. doi:10.4171/jst/267
apa: Dietlein, A. M., Gebert, M., & Müller, P. (2019). Perturbations of continuum
random Schrödinger operators with applications to Anderson orthogonality and the
spectral shift function. Journal of Spectral Theory. European Mathematical
Society Publishing House. https://doi.org/10.4171/jst/267
chicago: Dietlein, Adrian M, Martin Gebert, and Peter Müller. “Perturbations of
Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality
and the Spectral Shift Function.” Journal of Spectral Theory. European
Mathematical Society Publishing House, 2019. https://doi.org/10.4171/jst/267.
ieee: A. M. Dietlein, M. Gebert, and P. Müller, “Perturbations of continuum random
Schrödinger operators with applications to Anderson orthogonality and the spectral
shift function,” Journal of Spectral Theory, vol. 9, no. 3. European Mathematical
Society Publishing House, pp. 921–965, 2019.
ista: Dietlein AM, Gebert M, Müller P. 2019. Perturbations of continuum random Schrödinger
operators with applications to Anderson orthogonality and the spectral shift function.
Journal of Spectral Theory. 9(3), 921–965.
mla: Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger
Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.”
Journal of Spectral Theory, vol. 9, no. 3, European Mathematical Society
Publishing House, 2019, pp. 921–65, doi:10.4171/jst/267.
short: A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019)
921–965.
date_created: 2022-03-18T12:36:42Z
date_published: 2019-03-01T00:00:00Z
date_updated: 2023-09-08T11:35:31Z
day: '01'
department:
- _id: LaEr
doi: 10.4171/jst/267
external_id:
arxiv:
- '1701.02956'
isi:
- '000484709400006'
intvolume: ' 9'
isi: 1
issue: '3'
keyword:
- Random Schrödinger operators
- spectral shift function
- Anderson orthogonality
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1701.02956
month: '03'
oa: 1
oa_version: Preprint
page: 921-965
publication: Journal of Spectral Theory
publication_identifier:
issn:
- 1664-039X
publication_status: published
publisher: European Mathematical Society Publishing House
quality_controlled: '1'
scopus_import: '1'
status: public
title: Perturbations of continuum random Schrödinger operators with applications to
Anderson orthogonality and the spectral shift function
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 9
year: '2019'
...
---
_id: '8175'
abstract:
- lang: eng
text: We study edge asymptotics of poissonized Plancherel-type measures on skew
Young diagrams (integer partitions). These measures can be seen as generalizations
of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's
problem on longest increasing subsequences of random permutations and the last
passage percolation (corner growth) discrete versions thereof. Moreover they interpolate
between said measures and the uniform measure on partitions. In the new KPZ-like
1/3 exponent edge scaling limit with logarithmic corrections, we find new probability
distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions
from the theory of random matrices.
acknowledgement: "D.B. is especially grateful to Patrik Ferrari for suggesting simplifications
in Section 3 and\r\nto Alessandra Occelli for suggesting the name for the models
of Section 2.\r\n"
article_number: '34'
article_processing_charge: No
arxiv: 1
author:
- first_name: Dan
full_name: Betea, Dan
last_name: Betea
- first_name: Jérémie
full_name: Bouttier, Jérémie
last_name: Bouttier
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
- first_name: Mirjana
full_name: Vuletíc, Mirjana
last_name: Vuletíc
citation:
ama: 'Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young
diagrams via free boundaries. In: Proceedings on the 31st International Conference
on Formal Power Series and Algebraic Combinatorics. Formal Power Series and
Algebraic Combinatorics; 2019.'
apa: 'Betea, D., Bouttier, J., Nejjar, P., & Vuletíc, M. (2019). New edge asymptotics
of skew Young diagrams via free boundaries. In Proceedings on the 31st International
Conference on Formal Power Series and Algebraic Combinatorics. Ljubljana,
Slovenia: Formal Power Series and Algebraic Combinatorics.'
chicago: Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge
Asymptotics of Skew Young Diagrams via Free Boundaries.” In Proceedings on
the 31st International Conference on Formal Power Series and Algebraic Combinatorics.
Formal Power Series and Algebraic Combinatorics, 2019.
ieee: D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of
skew Young diagrams via free boundaries,” in Proceedings on the 31st International
Conference on Formal Power Series and Algebraic Combinatorics, Ljubljana,
Slovenia, 2019.
ista: 'Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew
Young diagrams via free boundaries. Proceedings on the 31st International Conference
on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference
on Formal Power Series and Algebraic Combinatorics, 34.'
mla: Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.”
Proceedings on the 31st International Conference on Formal Power Series and
Algebraic Combinatorics, 34, Formal Power Series and Algebraic Combinatorics,
2019.
short: D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st
International Conference on Formal Power Series and Algebraic Combinatorics, Formal
Power Series and Algebraic Combinatorics, 2019.
conference:
end_date: 2019-07-05
location: Ljubljana, Slovenia
name: 'FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics'
start_date: 2019-07-01
date_created: 2020-07-26T22:01:04Z
date_published: 2019-07-01T00:00:00Z
date_updated: 2021-01-12T08:17:18Z
day: '01'
department:
- _id: LaEr
ec_funded: 1
external_id:
arxiv:
- '1902.08750'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.08750
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Proceedings on the 31st International Conference on Formal Power Series
and Algebraic Combinatorics
publication_status: published
publisher: Formal Power Series and Algebraic Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: New edge asymptotics of skew Young diagrams via free boundaries
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '6843'
abstract:
- lang: eng
text: The aim of this short paper is to offer a complete characterization of all
(not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X),
where S is a countable discrete metric space and 0Journal of Mathematical Analysis and Applications.
2019;480(2). doi:10.1016/j.jmaa.2019.123435
apa: Gehér, G. P., Titkos, T., & Virosztek, D. (2019). On isometric embeddings
of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis
and Applications. Elsevier. https://doi.org/10.1016/j.jmaa.2019.123435
chicago: Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “On Isometric Embeddings
of Wasserstein Spaces – the Discrete Case.” Journal of Mathematical Analysis
and Applications. Elsevier, 2019. https://doi.org/10.1016/j.jmaa.2019.123435.
ieee: G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein
spaces – the discrete case,” Journal of Mathematical Analysis and Applications,
vol. 480, no. 2. Elsevier, 2019.
ista: Gehér GP, Titkos T, Virosztek D. 2019. On isometric embeddings of Wasserstein
spaces – the discrete case. Journal of Mathematical Analysis and Applications.
480(2), 123435.
mla: Gehér, György Pál, et al. “On Isometric Embeddings of Wasserstein Spaces –
the Discrete Case.” Journal of Mathematical Analysis and Applications,
vol. 480, no. 2, 123435, Elsevier, 2019, doi:10.1016/j.jmaa.2019.123435.
short: G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and
Applications 480 (2019).
date_created: 2019-09-01T22:01:01Z
date_published: 2019-12-15T00:00:00Z
date_updated: 2023-08-29T07:18:50Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.jmaa.2019.123435
ec_funded: 1
external_id:
arxiv:
- '1809.01101'
isi:
- '000486563900031'
intvolume: ' 480'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1809.01101
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Journal of Mathematical Analysis and Applications
publication_identifier:
eissn:
- '10960813'
issn:
- 0022247X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: On isometric embeddings of Wasserstein spaces – the discrete case
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 480
year: '2019'
...