---
_id: '405'
abstract:
- lang: eng
text: We investigate the quantum Jensen divergences from the viewpoint of joint
convexity. It turns out that the set of the functions which generate jointly convex
quantum Jensen divergences on positive matrices coincides with the Matrix Entropy
Class which has been introduced by Chen and Tropp quite recently.
acknowledgement: The author was supported by the ISTFELLOW program of the Institute
of Science and Technology Austria (project code IC1027FELL01) and partially supported
by the Hungarian National Research, Development and Innovation Office – NKFIH (grant
no. K124152)
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Virosztek D. Jointly convex quantum Jensen divergences. Linear Algebra and
Its Applications. 2019;576:67-78. doi:10.1016/j.laa.2018.03.002
apa: Virosztek, D. (2019). Jointly convex quantum Jensen divergences. Linear
Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2018.03.002
chicago: Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear
Algebra and Its Applications. Elsevier, 2019. https://doi.org/10.1016/j.laa.2018.03.002.
ieee: D. Virosztek, “Jointly convex quantum Jensen divergences,” Linear Algebra
and Its Applications, vol. 576. Elsevier, pp. 67–78, 2019.
ista: Virosztek D. 2019. Jointly convex quantum Jensen divergences. Linear Algebra
and Its Applications. 576, 67–78.
mla: Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra
and Its Applications, vol. 576, Elsevier, 2019, pp. 67–78, doi:10.1016/j.laa.2018.03.002.
short: D. Virosztek, Linear Algebra and Its Applications 576 (2019) 67–78.
corr_author: '1'
date_created: 2018-12-11T11:46:17Z
date_published: 2019-09-01T00:00:00Z
date_updated: 2025-04-15T06:50:00Z
day: '01'
department:
- _id: LaEr
doi: 10.1016/j.laa.2018.03.002
ec_funded: 1
external_id:
arxiv:
- '1712.05324'
isi:
- '000470955300005'
intvolume: ' 576'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1712.05324
month: '09'
oa: 1
oa_version: Preprint
page: 67-78
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Linear Algebra and Its Applications
publication_status: published
publisher: Elsevier
publist_id: '7424'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Jointly convex quantum Jensen divergences
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 576
year: '2019'
...
---
_id: '429'
abstract:
- lang: eng
text: We consider real symmetric or complex hermitian random matrices with correlated
entries. We prove local laws for the resolvent and universality of the local eigenvalue
statistics in the bulk of the spectrum. The correlations have fast decay but are
otherwise of general form. The key novelty is the detailed stability analysis
of the corresponding matrix valued Dyson equation whose solution is the deterministic
limit of the resolvent.
acknowledgement: "Open access funding provided by Institute of Science and Technology
(IST Austria).\r\n"
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Oskari H
full_name: Ajanki, Oskari H
id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
last_name: Ajanki
- 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: Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random
matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373.
doi:10.1007/s00440-018-0835-z
apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix
Dyson equation and random matrices with correlations. Probability Theory and
Related Fields. Springer. https://doi.org/10.1007/s00440-018-0835-z
chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the
Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory
and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0835-z.
ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation
and random matrices with correlations,” Probability Theory and Related Fields,
vol. 173, no. 1–2. Springer, pp. 293–373, 2019.
ista: Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation
and random matrices with correlations. Probability Theory and Related Fields.
173(1–2), 293–373.
mla: Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random
Matrices with Correlations.” Probability Theory and Related Fields, vol.
173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.
short: O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields
173 (2019) 293–373.
corr_author: '1'
date_created: 2018-12-11T11:46:25Z
date_published: 2019-02-01T00:00:00Z
date_updated: 2026-04-03T09:46:51Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-018-0835-z
ec_funded: 1
external_id:
isi:
- '000459396500007'
file:
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checksum: f9354fa5c71f9edd17132588f0dc7d01
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creator: dernst
date_created: 2018-12-17T16:12:08Z
date_updated: 2020-07-14T12:46:26Z
file_id: '5720'
file_name: 2018_ProbTheory_Ajanki.pdf
file_size: 1201840
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intvolume: ' 173'
isi: 1
issue: 1-2
language:
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month: '02'
oa: 1
oa_version: Published Version
page: 293–373
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
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name: IST Austria Open Access Fund
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer
publist_id: '7394'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stability of the matrix Dyson equation and random matrices with correlations
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 173
year: '2019'
...
---
OA_place: publisher
_id: '6179'
abstract:
- lang: eng
text: "In the first part of this thesis we consider large random matrices with arbitrary
expectation and a general slowly decaying correlation among its entries. We prove
universality of the local eigenvalue statistics and optimal local laws for the
resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic
control of a multivariate cumulant expansion.\r\nIn the second part we consider
Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue
distribution the local eigenvalue statistics are uni- versal 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. Our analysis
holds not only for exact cusps, but approximate cusps as well, where an ex- tended
Pearcey process emerges. As a main technical ingredient we prove an optimal local
law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow-
nian motion to the cusp regime.\r\nIn the third and final part we explore the
entrywise linear statistics of Wigner ma- trices and identify the fluctuations
for a large class of test functions with little regularity. This enables us to
study the rectangular Young diagram obtained from the interlacing eigenvalues
of the random matrix and its minor, and we find that, despite having the same
limit, the fluctuations differ from those of the algebraic Young tableaux equipped
with the Plancharel measure."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- 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: 'Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix
theory. 2019. doi:10.15479/AT:ISTA:th6179'
apa: 'Schröder, D. J. (2019). From Dyson to Pearcey: Universal statistics in
random matrix theory. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th6179'
chicago: 'Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random
Matrix Theory.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:th6179.'
ieee: 'D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix
theory,” Institute of Science and Technology Austria, 2019.'
ista: 'Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random
matrix theory. Institute of Science and Technology Austria.'
mla: 'Schröder, Dominik J. From Dyson to Pearcey: Universal Statistics in Random
Matrix Theory. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:th6179.'
short: 'D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix
Theory, Institute of Science and Technology Austria, 2019.'
corr_author: '1'
date_created: 2019-03-28T08:58:59Z
date_published: 2019-03-18T00:00:00Z
date_updated: 2026-04-08T13:55:03Z
day: '18'
ddc:
- '515'
- '519'
degree_awarded: PhD
department:
- _id: LaEr
doi: 10.15479/AT:ISTA:th6179
ec_funded: 1
file:
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creator: dernst
date_created: 2019-03-28T08:53:52Z
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file_name: 2019_Schroeder_Thesis.tar.gz
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file_name: 2019_Schroeder_Thesis.pdf
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language:
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month: '03'
oa: 1
oa_version: Published Version
page: '375'
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '6184'
relation: part_of_dissertation
status: public
- id: '6186'
relation: part_of_dissertation
status: public
- id: '6185'
relation: part_of_dissertation
status: public
- id: '1012'
relation: part_of_dissertation
status: public
- id: '1144'
relation: part_of_dissertation
status: public
- id: '6182'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
title: 'From Dyson to Pearcey: Universal statistics in random matrix theory'
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2019'
...
---
_id: '6182'
abstract:
- lang: eng
text: "We consider large random matrices with a general slowly decaying correlation
among its entries. We prove universality of the local eigenvalue statistics and
optimal local laws for the resolvent away from the spectral edges, generalizing
the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and
random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019),
293–373] to allow slow correlation decay and arbitrary expectation. The main novel
tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion."
article_number: e8
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: 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. Random matrices with slow correlation decay.
Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2
apa: Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with
slow correlation decay. Forum of Mathematics, Sigma. Cambridge University
Press. https://doi.org/10.1017/fms.2019.2
chicago: Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices
with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University
Press, 2019. https://doi.org/10.1017/fms.2019.2.
ieee: L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation
decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press,
2019.
ista: Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation
decay. Forum of Mathematics, Sigma. 7, e8.
mla: Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” Forum
of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2.
short: L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).
corr_author: '1'
date_created: 2019-03-28T09:05:23Z
date_published: 2019-03-26T00:00:00Z
date_updated: 2026-04-08T13:55:03Z
day: '26'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2019.2
ec_funded: 1
external_id:
arxiv:
- '1705.10661'
isi:
- '000488847100001'
file:
- access_level: open_access
checksum: 933a472568221c73b2c3ce8c87bf6d15
content_type: application/pdf
creator: dernst
date_created: 2019-09-17T14:24:13Z
date_updated: 2020-07-14T12:47:22Z
file_id: '6883'
file_name: 2019_Forum_Erdoes.pdf
file_size: 1520344
relation: main_file
file_date_updated: 2020-07-14T12:47:22Z
has_accepted_license: '1'
intvolume: ' 7'
isi: 1
language:
- iso: eng
month: '03'
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:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Random matrices with slow correlation decay
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 7
year: '2019'
...
---
_id: '6186'
abstract:
- lang: eng
text: "We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices
near the cusp points of the eigenvalue density are universal. Together\r\nwith
the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe
complex Hermitian symmetry class, this completes the last remaining case of\r\nthe
Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities
have been established in the last years. We extend the recent\r\nDyson Brownian
motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the
optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis
of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a
PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum
principle of the heat flow related to the Dyson\r\nBrownian motion."
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: 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: 'Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random
matrices, II: The real symmetric case. Pure and Applied Analysis . 2019;1(4):615–707.
doi:10.2140/paa.2019.1.615'
apa: 'Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Cusp
universality for random matrices, II: The real symmetric case. Pure and Applied
Analysis . MSP. https://doi.org/10.2140/paa.2019.1.615'
chicago: 'Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder.
“Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure
and Applied Analysis . MSP, 2019. https://doi.org/10.2140/paa.2019.1.615.'
ieee: 'G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality
for random matrices, II: The real symmetric case,” Pure and Applied Analysis
, vol. 1, no. 4. MSP, pp. 615–707, 2019.'
ista: 'Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for
random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4),
615–707.'
mla: 'Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The
Real Symmetric Case.” Pure and Applied Analysis , vol. 1, no. 4, MSP, 2019,
pp. 615–707, doi:10.2140/paa.2019.1.615.'
short: G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1
(2019) 615–707.
date_created: 2019-03-28T10:21:17Z
date_published: 2019-10-12T00:00:00Z
date_updated: 2026-04-08T13:55:02Z
day: '12'
department:
- _id: LaEr
doi: 10.2140/paa.2019.1.615
ec_funded: 1
external_id:
arxiv:
- '1811.04055'
intvolume: ' 1'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1811.04055
month: '10'
oa: 1
oa_version: Preprint
page: 615–707
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: 'Pure and Applied Analysis '
publication_identifier:
eissn:
- 2578-5885
issn:
- 2578-5893
publication_status: published
publisher: MSP
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: 'Cusp universality for random matrices, II: The real symmetric case'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2019'
...
---
_id: '6240'
abstract:
- lang: eng
text: For a general class of large non-Hermitian random block matrices X we prove
that there are no eigenvalues away from a deterministic set with very high probability.
This set is obtained from the Dyson equation of the Hermitization of X as the
self-consistent approximation of the pseudospectrum. We demonstrate that the analysis
of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers
a unified treatment of many structured matrix ensembles.
article_processing_charge: No
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: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker
random matrices. Annales de l’institut Henri Poincare. 2019;55(2):661-696.
doi:10.1214/18-AIHP894
apa: Alt, J., Erdös, L., Krüger, T. H., & Nemish, Y. (2019). Location of the
spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare.
Institut Henri Poincaré. https://doi.org/10.1214/18-AIHP894
chicago: Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location
of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri
Poincare. Institut Henri Poincaré, 2019. https://doi.org/10.1214/18-AIHP894.
ieee: J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of
Kronecker random matrices,” Annales de l’institut Henri Poincare, vol.
55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.
ista: Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker
random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696.
mla: Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.”
Annales de l’institut Henri Poincare, vol. 55, no. 2, Institut Henri Poincaré,
2019, pp. 661–96, doi:10.1214/18-AIHP894.
short: J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare
55 (2019) 661–696.
date_created: 2019-04-08T14:05:04Z
date_published: 2019-05-01T00:00:00Z
date_updated: 2026-04-08T14:11:36Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/18-AIHP894
ec_funded: 1
external_id:
arxiv:
- '1706.08343'
isi:
- '000467793600003'
intvolume: ' 55'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1706.08343
month: '05'
oa: 1
oa_version: Preprint
page: 661-696
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Annales de l'institut Henri Poincare
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institut Henri Poincaré
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Location of the spectrum of Kronecker random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2019'
...
---
_id: '284'
abstract:
- lang: eng
text: "Borel probability measures living on metric spaces are fundamental\r\nmathematical
objects. There are several meaningful distance functions that make the collection
of the probability measures living on a certain space a metric space. We are interested
in the description of the structure of the isometries of such metric spaces. We
overview some of the recent results of the topic and we also provide some new
ones concerning the Wasserstein distance. More specifically, we consider the space
of all Borel probability measures on the unit sphere of a Euclidean space endowed
with the Wasserstein metric W_p for arbitrary p >= 1, and we show that the
action of a Wasserstein isometry on the set of Dirac measures is induced by an
isometry of the underlying unit sphere."
acknowledgement: The author was supported by the ISTFELLOW program of the Institute
of Science and Technol- ogy Austria (project code IC1027FELL01) and partially supported
by the Hungarian National Research, Development and Innovation Office, NKFIH (grant
no. K124152).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Virosztek D. Maps on probability measures preserving certain distances - a
survey and some new results. Acta Scientiarum Mathematicarum. 2018;84(1-2):65-80.
doi:10.14232/actasm-018-753-y
apa: Virosztek, D. (2018). Maps on probability measures preserving certain distances
- a survey and some new results. Acta Scientiarum Mathematicarum. Springer
Nature. https://doi.org/10.14232/actasm-018-753-y
chicago: Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances
- a Survey and Some New Results.” Acta Scientiarum Mathematicarum. Springer
Nature, 2018. https://doi.org/10.14232/actasm-018-753-y.
ieee: D. Virosztek, “Maps on probability measures preserving certain distances -
a survey and some new results,” Acta Scientiarum Mathematicarum, vol. 84,
no. 1–2. Springer Nature, pp. 65–80, 2018.
ista: Virosztek D. 2018. Maps on probability measures preserving certain distances
- a survey and some new results. Acta Scientiarum Mathematicarum. 84(1–2), 65–80.
mla: Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances
- a Survey and Some New Results.” Acta Scientiarum Mathematicarum, vol.
84, no. 1–2, Springer Nature, 2018, pp. 65–80, doi:10.14232/actasm-018-753-y.
short: D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80.
date_created: 2018-12-11T11:45:36Z
date_published: 2018-06-04T00:00:00Z
date_updated: 2025-04-15T06:50:21Z
day: '04'
department:
- _id: LaEr
doi: 10.14232/actasm-018-753-y
ec_funded: 1
external_id:
arxiv:
- '1802.03305'
intvolume: ' 84'
issue: 1-2
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1802.03305
month: '06'
oa: 1
oa_version: Preprint
page: 65 - 80
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Acta Scientiarum Mathematicarum
publication_identifier:
eissn:
- 2064-8316
issn:
- 0001-6969
publication_status: published
publisher: Springer Nature
publist_id: '7615'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maps on probability measures preserving certain distances - a survey and some
new results
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 84
year: '2018'
...
---
_id: '181'
abstract:
- lang: eng
text: We consider large random matrices X with centered, independent entries but
possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for
f, g functions analytic on the spectrum of X. We use these results to compute
the long time asymptotics for systems of coupled di erential equations with random
coe cients. We show that when the coupling is critical, the norm squared of the
solution decays like t−1/2.
acknowledgement: The work of the second author was also partially supported by the
Hausdorff Center of Mathematics.
article_processing_charge: No
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: David T
full_name: Renfrew, David T
id: 4845BF6A-F248-11E8-B48F-1D18A9856A87
last_name: Renfrew
orcid: 0000-0003-3493-121X
citation:
ama: Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled
differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290.
doi:10.1137/17M1143125
apa: Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for
systems of randomly coupled differential equations. SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125
chicago: Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for
Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125.
ieee: L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of
randomly coupled differential equations,” SIAM Journal on Mathematical Analysis,
vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290,
2018.
ista: Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly
coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3),
3271–3290.
mla: Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential
Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society
for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125.
short: L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis
50 (2018) 3271–3290.
date_created: 2018-12-11T11:45:03Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2025-04-15T08:05:02Z
day: '01'
department:
- _id: LaEr
doi: 10.1137/17M1143125
ec_funded: 1
external_id:
arxiv:
- '1708.01546'
isi:
- '000437018500032'
intvolume: ' 50'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.01546
month: '01'
oa: 1
oa_version: Published Version
page: 3271 - 3290
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 258F40A4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02080
name: Structured Non-Hermitian Random Matrices
publication: SIAM Journal on Mathematical Analysis
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7740'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Power law decay for systems of randomly coupled differential equations
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 50
year: '2018'
...
---
_id: '556'
abstract:
- lang: eng
text: 'We investigate the free boundary Schur process, a variant of the Schur process
introduced by Okounkov and Reshetikhin, where we allow the first and the last
partitions to be arbitrary (instead of empty in the original setting). The pfaffian
Schur process, previously studied by several authors, is recovered when just one
of the boundary partitions is left free. We compute the correlation functions
of the process in all generality via the free fermion formalism, which we extend
with the thorough treatment of “free boundary states.” For the case of one free
boundary, our approach yields a new proof that the process is pfaffian. For the
case of two free boundaries, we find that the process is not pfaffian, but a closely
related process is. We also study three different applications of the Schur process
with one free boundary: fluctuations of symmetrized last passage percolation models,
limit shapes and processes for symmetric plane partitions and for plane overpartitions.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Dan
full_name: Betea, Dan
last_name: Betea
- first_name: Jeremie
full_name: Bouttier, Jeremie
last_name: Bouttier
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
- first_name: Mirjana
full_name: Vuletic, Mirjana
last_name: Vuletic
citation:
ama: Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and
applications I. Annales Henri Poincare. 2018;19(12):3663-3742. doi:10.1007/s00023-018-0723-1
apa: Betea, D., Bouttier, J., Nejjar, P., & Vuletic, M. (2018). The free boundary
Schur process and applications I. Annales Henri Poincare. Springer Nature.
https://doi.org/10.1007/s00023-018-0723-1
chicago: Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free
Boundary Schur Process and Applications I.” Annales Henri Poincare. Springer
Nature, 2018. https://doi.org/10.1007/s00023-018-0723-1.
ieee: D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur
process and applications I,” Annales Henri Poincare, vol. 19, no. 12. Springer
Nature, pp. 3663–3742, 2018.
ista: Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process
and applications I. Annales Henri Poincare. 19(12), 3663–3742.
mla: Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” Annales
Henri Poincare, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:10.1007/s00023-018-0723-1.
short: D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018)
3663–3742.
date_created: 2018-12-11T11:47:09Z
date_published: 2018-11-13T00:00:00Z
date_updated: 2025-09-18T07:34:29Z
day: '13'
ddc:
- '500'
department:
- _id: LaEr
- _id: JaMa
doi: 10.1007/s00023-018-0723-1
ec_funded: 1
external_id:
arxiv:
- '1704.05809'
isi:
- '000450487900003'
file:
- access_level: open_access
checksum: 0c38abe73569b7166b7487ad5d23cc68
content_type: application/pdf
creator: dernst
date_created: 2019-01-21T15:18:55Z
date_updated: 2020-07-14T12:47:03Z
file_id: '5866'
file_name: 2018_Annales_Betea.pdf
file_size: 3084674
relation: main_file
file_date_updated: 2020-07-14T12:47:03Z
has_accepted_license: '1'
intvolume: ' 19'
isi: 1
issue: '12'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 3663-3742
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: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
publist_id: '7258'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The free boundary Schur process and applications I
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 19
year: '2018'
...
---
_id: '5971'
abstract:
- lang: eng
text: "We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices
H=H∗ with centered independent entries and with a general matrix of variances
Sxy=\U0001D53C∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of
the support of the self-consistent density of states. We establish a bound on
this maximum in terms of norms of powers of S that substantially improves the
earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality
for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727].
The key element of the proof is an effective Markov chain approximation for the
contributions of the weighted Dyck paths appearing in the iterative solution of
the corresponding Dyson equation."
article_number: '1950009'
article_processing_charge: No
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: Peter
full_name: Mühlbacher, Peter
last_name: Mühlbacher
citation:
ama: 'Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices.
Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096'
apa: 'Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type
random matrices. Random Matrices: Theory and Applications. World Scientific
Publishing. https://doi.org/10.1142/s2010326319500096'
chicago: 'Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type
Random Matrices.” Random Matrices: Theory and Applications. World Scientific
Publishing, 2018. https://doi.org/10.1142/s2010326319500096.'
ieee: 'L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,”
Random matrices: Theory and applications. World Scientific Publishing,
2018.'
ista: 'Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices.
Random matrices: Theory and applications., 1950009.'
mla: 'Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random
Matrices.” Random Matrices: Theory and Applications, 1950009, World Scientific
Publishing, 2018, doi:10.1142/s2010326319500096.'
short: 'L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).'
date_created: 2019-02-13T10:40:54Z
date_published: 2018-09-26T00:00:00Z
date_updated: 2025-04-15T08:05:02Z
day: '26'
department:
- _id: LaEr
doi: 10.1142/s2010326319500096
ec_funded: 1
external_id:
arxiv:
- '1802.05175'
isi:
- '000477677200002'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1802.05175
month: '09'
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: 'Random matrices: Theory and applications'
publication_identifier:
eissn:
- 2010-3271
issn:
- 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bounds on the norm of Wigner-type random matrices
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...
---
_id: '690'
abstract:
- lang: eng
text: We consider spectral properties and the edge universality of sparse random
matrices, the class of random matrices that includes the adjacency matrices of
the Erdős–Rényi graph model G(N, p). We prove a local law for the eigenvalue density
up to the spectral edges. Under a suitable condition on the sparsity, we also
prove that the rescaled extremal eigenvalues exhibit GOE Tracy–Widom fluctuations
if a deterministic shift of the spectral edge due to the sparsity is included.
For the adjacency matrix of the Erdős–Rényi graph this establishes the Tracy–Widom
fluctuations of the second largest eigenvalue when p is much larger than N−2/3
with a deterministic shift of order (Np)−1.
article_number: 543-616
article_processing_charge: No
arxiv: 1
author:
- first_name: Jii
full_name: Lee, Jii
last_name: Lee
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Lee J, Schnelli K. Local law and Tracy–Widom limit for sparse random matrices.
Probability Theory and Related Fields. 2018;171(1-2). doi:10.1007/s00440-017-0787-8
apa: Lee, J., & Schnelli, K. (2018). Local law and Tracy–Widom limit for sparse
random matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-017-0787-8
chicago: Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse
Random Matrices.” Probability Theory and Related Fields. Springer, 2018.
https://doi.org/10.1007/s00440-017-0787-8.
ieee: J. Lee and K. Schnelli, “Local law and Tracy–Widom limit for sparse random
matrices,” Probability Theory and Related Fields, vol. 171, no. 1–2. Springer,
2018.
ista: Lee J, Schnelli K. 2018. Local law and Tracy–Widom limit for sparse random
matrices. Probability Theory and Related Fields. 171(1–2), 543–616.
mla: Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random
Matrices.” Probability Theory and Related Fields, vol. 171, no. 1–2, 543–616,
Springer, 2018, doi:10.1007/s00440-017-0787-8.
short: J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018).
date_created: 2018-12-11T11:47:56Z
date_published: 2018-06-14T00:00:00Z
date_updated: 2025-09-10T14:00:58Z
day: '14'
department:
- _id: LaEr
doi: 10.1007/s00440-017-0787-8
ec_funded: 1
external_id:
arxiv:
- '1605.08767'
isi:
- '000432129600012'
intvolume: ' 171'
isi: 1
issue: 1-2
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1605.08767
month: '06'
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: Probability Theory and Related Fields
publication_status: published
publisher: Springer
publist_id: '7017'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local law and Tracy–Widom limit for sparse random matrices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 171
year: '2018'
...
---
_id: '70'
abstract:
- lang: eng
text: We consider the totally asymmetric simple exclusion process in a critical
scaling parametrized by a≥0, which creates a shock in the particle density of
order aT−1/3, T the observation time. When starting from step initial data, we
provide bounds on the limiting law which in particular imply that in the double
limit lima→∞limT→∞ one recovers the product limit law and the degeneration of
the correlation length observed at shocks of order 1. This result is shown to
apply to a general last-passage percolation model. We also obtain bounds on the
two-point functions of several airy processes.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
citation:
ama: Nejjar P. Transition to shocks in TASEP and decoupling of last passage times.
Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334.
doi:10.30757/ALEA.v15-49
apa: Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage
times. Latin American Journal of Probability and Mathematical Statistics.
Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49
chicago: Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage
Times.” Latin American Journal of Probability and Mathematical Statistics.
Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49.
ieee: P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,”
Latin American Journal of Probability and Mathematical Statistics, vol.
15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.
ista: Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage
times. Latin American Journal of Probability and Mathematical Statistics. 15(2),
1311–1334.
mla: Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage
Times.” Latin American Journal of Probability and Mathematical Statistics,
vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34,
doi:10.30757/ALEA.v15-49.
short: P. Nejjar, Latin American Journal of Probability and Mathematical Statistics
15 (2018) 1311–1334.
date_created: 2018-12-11T11:44:28Z
date_published: 2018-10-01T00:00:00Z
date_updated: 2025-04-14T07:27:49Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
- _id: JaMa
doi: 10.30757/ALEA.v15-49
ec_funded: 1
external_id:
arxiv:
- '1705.08836'
isi:
- '000460475800022'
file:
- access_level: open_access
checksum: 2ded46aa284a836a8cbb34133a64f1cb
content_type: application/pdf
creator: kschuh
date_created: 2019-02-14T09:44:10Z
date_updated: 2020-07-14T12:47:46Z
file_id: '5981'
file_name: 2018_ALEA_Nejjar.pdf
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oa: 1
oa_version: Published Version
page: 1311-1334
project:
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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: Latin American Journal of Probability and Mathematical Statistics
publication_identifier:
issn:
- 1980-0436
publication_status: published
publisher: Instituto Nacional de Matematica Pura e Aplicada
quality_controlled: '1'
scopus_import: '1'
status: public
title: Transition to shocks in TASEP and decoupling of last passage times
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2018'
...
---
_id: '1012'
abstract:
- lang: eng
text: We prove a new central limit theorem (CLT) for the difference of linear eigenvalue
statistics of a Wigner random matrix H and its minor H and find that the fluctuation
is much smaller than the fluctuations of the individual linear statistics, as
a consequence of the strong correlation between the eigenvalues of H and H. In
particular, our theorem identifies the fluctuation of Kerov's rectangular Young
diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic
shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel
measure follow the same limiting shape. For this, algebraically motivated, ensemble
a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar
to our result but the variance is different, indicating that the analogy between
the two models has its limitations. Moreover, our theorem shows that Borodin's
result [7] on the convergence of the spectral distribution of Wigner matrices
to a Gaussian free field also holds in derivative sense.
article_processing_charge: No
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: 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, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing
wigner eigenvalues. International Mathematics Research Notices. 2018;2018(10):3255-3298.
doi:10.1093/imrn/rnw330
apa: Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young
diagrams of interlacing wigner eigenvalues. International Mathematics Research
Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnw330
chicago: Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young
Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research
Notices. Oxford University Press, 2018. https://doi.org/10.1093/imrn/rnw330.
ieee: L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of
interlacing wigner eigenvalues,” International Mathematics Research Notices,
vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.
ista: Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of
interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10),
3255–3298.
mla: Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young
Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research
Notices, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:10.1093/imrn/rnw330.
short: L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018
(2018) 3255–3298.
date_created: 2018-12-11T11:49:41Z
date_published: 2018-05-18T00:00:00Z
date_updated: 2026-04-08T13:55:03Z
day: '18'
department:
- _id: LaEr
doi: 10.1093/imrn/rnw330
ec_funded: 1
external_id:
arxiv:
- '1608.05163'
isi:
- '000441668300009'
intvolume: ' 2018'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.05163
month: '05'
oa: 1
oa_version: Preprint
page: 3255-3298
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: International Mathematics Research Notices
publication_identifier:
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
publist_id: '6383'
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2018
year: '2018'
...
---
OA_place: publisher
_id: '149'
abstract:
- lang: eng
text: The eigenvalue density of many large random matrices is well approximated
by a deterministic measure, the self-consistent density of states. In the present
work, we show this behaviour for several classes of random matrices. In fact,
we establish that, in each of these classes, the self-consistent density of states
approximates the eigenvalue density of the random matrix on all scales slightly
above the typical eigenvalue spacing. For large classes of random matrices, the
self-consistent density of states exhibits several universal features. We prove
that, under suitable assumptions, random Gram matrices and Hermitian random matrices
with decaying correlations have a 1/3-Hölder continuous self-consistent density
of states ρ on R, which is analytic, where it is positive, and has either a square
root edge or a cubic root cusp, where it vanishes. We, thus, extend the validity
of the corresponding result for Wigner-type matrices from [4, 5, 7]. We show that
ρ is determined as the inverse Stieltjes transform of the normalized trace of
the unique solution m(z) to the Dyson equation −m(z) −1 = z − a + S[m(z)] on C
N×N with the constraint Im m(z) ≥ 0. Here, z lies in the complex upper half-plane,
a is a self-adjoint element of C N×N and S is a positivity-preserving operator
on C N×N encoding the first two moments of the random matrix. In order to analyze
a possible limit of ρ for N → ∞ and address some applications in free probability
theory, we also consider the Dyson equation on infinite dimensional von Neumann
algebras. We present two applications to random matrices. We first establish that,
under certain assumptions, large random matrices with independent entries have
a rotationally symmetric self-consistent density of states which is supported
on a centered disk in C. Moreover, it is infinitely often differentiable apart
from a jump on the boundary of this disk. Second, we show edge universality at
all regular (not necessarily extreme) spectral edges for Hermitian random matrices
with decaying correlations.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
citation:
ama: Alt J. Dyson equation and eigenvalue statistics of random matrices. 2018. doi:10.15479/AT:ISTA:TH_1040
apa: Alt, J. (2018). Dyson equation and eigenvalue statistics of random matrices.
Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:TH_1040
chicago: Alt, Johannes. “Dyson Equation and Eigenvalue Statistics of Random Matrices.”
Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:TH_1040.
ieee: J. Alt, “Dyson equation and eigenvalue statistics of random matrices,” Institute
of Science and Technology Austria, 2018.
ista: Alt J. 2018. Dyson equation and eigenvalue statistics of random matrices.
Institute of Science and Technology Austria.
mla: Alt, Johannes. Dyson Equation and Eigenvalue Statistics of Random Matrices.
Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:TH_1040.
short: J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, Institute
of Science and Technology Austria, 2018.
corr_author: '1'
date_created: 2018-12-11T11:44:53Z
date_published: 2018-07-12T00:00:00Z
date_updated: 2026-04-08T14:11:37Z
day: '12'
ddc:
- '515'
- '519'
degree_awarded: PhD
department:
- _id: LaEr
doi: 10.15479/AT:ISTA:TH_1040
ec_funded: 1
file:
- access_level: open_access
checksum: d4dad55a7513f345706aaaba90cb1bb8
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oa_version: Published Version
page: '456'
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '7772'
pubrep_id: '1040'
related_material:
record:
- id: '6240'
relation: part_of_dissertation
status: public
- id: '6184'
relation: part_of_dissertation
status: public
- id: '566'
relation: part_of_dissertation
status: public
- id: '6183'
relation: part_of_dissertation
status: public
- id: '1010'
relation: part_of_dissertation
status: public
- id: '550'
relation: part_of_dissertation
status: public
- id: '1677'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
title: Dyson equation and eigenvalue statistics of random 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: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2018'
...
---
_id: '566'
abstract:
- lang: eng
text: "We consider large random matrices X with centered, independent entries which
have comparable but not necessarily identical variances. Girko's circular law
asserts that the spectrum is supported in a disk and in case of identical variances,
the limiting density is uniform. In this special case, the local circular law
by Bourgade et. al. [11,12] shows that the empirical density converges even locally
on scales slightly above the typical eigenvalue spacing. In the general case,
the limiting density is typically inhomogeneous and it is obtained via solving
a system of deterministic equations. Our main result is the local inhomogeneous
circular law in the bulk spectrum on the optimal scale for a general variance
profile of the entries of X. \r\n\r\n"
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
citation:
ama: Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. Annals Applied
Probability . 2018;28(1):148-203. doi:10.1214/17-AAP1302
apa: Alt, J., Erdös, L., & Krüger, T. H. (2018). Local inhomogeneous circular
law. Annals Applied Probability . Institute of Mathematical Statistics.
https://doi.org/10.1214/17-AAP1302
chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Local Inhomogeneous
Circular Law.” Annals Applied Probability . Institute of Mathematical Statistics,
2018. https://doi.org/10.1214/17-AAP1302.
ieee: J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals
Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics,
pp. 148–203, 2018.
ista: Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals
Applied Probability . 28(1), 148–203.
mla: Alt, Johannes, et al. “Local Inhomogeneous Circular Law.” Annals Applied
Probability , vol. 28, no. 1, Institute of Mathematical Statistics, 2018,
pp. 148–203, doi:10.1214/17-AAP1302.
short: J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203.
corr_author: '1'
date_created: 2018-12-11T11:47:13Z
date_published: 2018-03-03T00:00:00Z
date_updated: 2026-04-08T14:11:36Z
day: '03'
department:
- _id: LaEr
doi: 10.1214/17-AAP1302
ec_funded: 1
external_id:
arxiv:
- '1612.07776 '
isi:
- '000431721800005'
intvolume: ' 28'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 'https://arxiv.org/abs/1612.07776 '
month: '03'
oa: 1
oa_version: Preprint
page: 148-203
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: 'Annals Applied Probability '
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Local inhomogeneous circular law
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 28
year: '2018'
...
---
_id: '6183'
abstract:
- lang: eng
text: "We study the unique solution $m$ of the Dyson equation \\[ -m(z)^{-1} = z
- a\r\n+ S[m(z)] \\] on a von Neumann algebra $\\mathcal{A}$ with the constraint\r\n$\\mathrm{Im}\\,m\\geq
0$. Here, $z$ lies in the complex upper half-plane, $a$ is\r\na self-adjoint element
of $\\mathcal{A}$ and $S$ is a positivity-preserving\r\nlinear operator on $\\mathcal{A}$.
We show that $m$ is the Stieltjes transform\r\nof a compactly supported $\\mathcal{A}$-valued
measure on $\\mathbb{R}$. Under\r\nsuitable assumptions, we establish that this
measure has a uniformly\r\n$1/3$-H\\\"{o}lder continuous density with respect
to the Lebesgue measure, which\r\nis supported on finitely many intervals, called
bands. In fact, the density is\r\nanalytic inside the bands with a square-root
growth at the edges and internal\r\ncubic root cusps whenever the gap between
two bands vanishes. The shape of\r\nthese singularities is universal and no other
singularity may occur. We give a\r\nprecise asymptotic description of $m$ near
the singular points. These\r\nasymptotics generalize the analysis at the regular
edges given in the companion\r\npaper on the Tracy-Widom universality for the
edge eigenvalue statistics for\r\ncorrelated random matrices [arXiv:1804.07744]
and they play a key role in the\r\nproof of the Pearcey universality at the cusp
for Wigner-type matrices\r\n[arXiv:1809.03971,arXiv:1811.04055]. We also extend
the finite dimensional band\r\nmass formula from [arXiv:1804.07744] to the von
Neumann algebra setting by\r\nshowing that the spectral mass of the bands is topologically
rigid under\r\ndeformations and we conclude that these masses are quantized in
some important\r\ncases."
acknowledgement: "Partially funded by ERC Advanced Grant RANMAT No. 338804.\r\nPartially
supported by the Hausdorff Center for Mathematics.\r\n"
article_number: '1804.07752'
article_processing_charge: No
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. arXiv. doi:10.48550/arXiv.1804.07752'
apa: 'Alt, J., Erdös, L., & Krüger, T. H. (n.d.). The Dyson equation with linear
self-energy: Spectral bands, edges and cusps. arXiv. https://doi.org/10.48550/arXiv.1804.07752'
chicago: 'Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation
with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, n.d.
https://doi.org/10.48550/arXiv.1804.07752.'
ieee: 'J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy:
Spectral bands, edges and cusps,” arXiv. .'
ista: 'Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral
bands, edges and cusps. arXiv, 1804.07752.'
mla: 'Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral
Bands, Edges and Cusps.” ArXiv, 1804.07752, doi:10.48550/arXiv.1804.07752.'
short: J. Alt, L. Erdös, T.H. Krüger, ArXiv (n.d.).
date_created: 2019-03-28T09:20:06Z
date_published: 2018-04-20T00:00:00Z
date_updated: 2026-04-08T14:11:36Z
day: '20'
department:
- _id: LaEr
doi: 10.48550/arXiv.1804.07752
ec_funded: 1
external_id:
arxiv:
- '1804.07752'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.07752
month: '04'
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: arXiv
publication_status: draft
related_material:
record:
- id: '14694'
relation: later_version
status: public
- id: '149'
relation: dissertation_contains
status: public
status: public
title: 'The Dyson equation with linear self-energy: Spectral bands, edges and cusps'
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '1207'
abstract:
- lang: eng
text: The eigenvalue distribution of the sum of two large Hermitian matrices, when
one of them is conjugated by a Haar distributed unitary matrix, is asymptotically
given by the free convolution of their spectral distributions. We prove that this
convergence also holds locally in the bulk of the spectrum, down to the optimal
scales larger than the eigenvalue spacing. The corresponding eigenvectors are
fully delocalized. Similar results hold for the sum of two real symmetric matrices,
when one is conjugated by Haar orthogonal matrix.
article_processing_charge: Yes (via OA deal)
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. Local law of addition of random matrices on optimal
scale. Communications in Mathematical Physics. 2017;349(3):947-990. doi:10.1007/s00220-016-2805-6
apa: Bao, Z., Erdös, L., & Schnelli, K. (2017). Local law of addition of random
matrices on optimal scale. Communications in Mathematical Physics. Springer.
https://doi.org/10.1007/s00220-016-2805-6
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition
of Random Matrices on Optimal Scale.” Communications in Mathematical Physics.
Springer, 2017. https://doi.org/10.1007/s00220-016-2805-6.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices
on optimal scale,” Communications in Mathematical Physics, vol. 349, no.
3. Springer, pp. 947–990, 2017.
ista: Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices
on optimal scale. Communications in Mathematical Physics. 349(3), 947–990.
mla: Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.”
Communications in Mathematical Physics, vol. 349, no. 3, Springer, 2017,
pp. 947–90, doi:10.1007/s00220-016-2805-6.
short: Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349
(2017) 947–990.
date_created: 2018-12-11T11:50:43Z
date_published: 2017-02-01T00:00:00Z
date_updated: 2025-07-10T11:50:22Z
day: '01'
ddc:
- '530'
department:
- _id: LaEr
doi: 10.1007/s00220-016-2805-6
ec_funded: 1
external_id:
isi:
- '000393696700005'
file:
- access_level: open_access
checksum: ddff79154c3daf27237de5383b1264a9
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:14:47Z
date_updated: 2020-07-14T12:44:39Z
file_id: '5102'
file_name: IST-2016-722-v1+1_s00220-016-2805-6.pdf
file_size: 1033743
relation: main_file
file_date_updated: 2020-07-14T12:44:39Z
has_accepted_license: '1'
intvolume: ' 349'
isi: 1
issue: '3'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 947 - 990
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
publication_status: published
publisher: Springer
publist_id: '6141'
pubrep_id: '722'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local law of addition of random matrices on optimal scale
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: 349
year: '2017'
...
---
_id: '1023'
abstract:
- lang: eng
text: We consider products of independent square non-Hermitian random matrices.
More precisely, let X1,…, Xn be independent N × N random matrices with independent
entries (real or complex with independent real and imaginary parts) with zero
mean and variance 1/N. Soshnikov-O’Rourke [19] and Götze-Tikhomirov [15] showed
that the empirical spectral distribution of the product of n random matrices with
iid entries converges to (equation found). We prove that if the entries of the
matrices X1,…, Xn are independent (but not necessarily identically distributed)
and satisfy uniform subexponential decay condition, then in the bulk the convergence
of the ESD of X1,…, Xn to (0.1) holds up to the scale N–1/2+ε.
article_number: '22'
article_processing_charge: No
author:
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Nemish Y. Local law for the product of independent non-Hermitian random matrices
with independent entries. Electronic Journal of Probability. 2017;22. doi:10.1214/17-EJP38
apa: Nemish, Y. (2017). Local law for the product of independent non-Hermitian random
matrices with independent entries. Electronic Journal of Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/17-EJP38
chicago: Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian
Random Matrices with Independent Entries.” Electronic Journal of Probability.
Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-EJP38.
ieee: Y. Nemish, “Local law for the product of independent non-Hermitian random
matrices with independent entries,” Electronic Journal of Probability,
vol. 22. Institute of Mathematical Statistics, 2017.
ista: Nemish Y. 2017. Local law for the product of independent non-Hermitian random
matrices with independent entries. Electronic Journal of Probability. 22, 22.
mla: Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random
Matrices with Independent Entries.” Electronic Journal of Probability,
vol. 22, 22, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP38.
short: Y. Nemish, Electronic Journal of Probability 22 (2017).
date_created: 2018-12-11T11:49:44Z
date_published: 2017-02-06T00:00:00Z
date_updated: 2025-07-10T11:49:47Z
day: '06'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/17-EJP38
external_id:
isi:
- '000396611900022'
file:
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content_type: application/pdf
creator: system
date_created: 2018-12-12T10:15:29Z
date_updated: 2018-12-12T10:15:29Z
file_id: '5149'
file_name: IST-2017-802-v1+1_euclid.ejp.1487991681.pdf
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file_date_updated: 2018-12-12T10:15:29Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
publication: Electronic Journal of Probability
publication_identifier:
issn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6370'
pubrep_id: '802'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local law for the product of independent non-Hermitian random matrices with
independent entries
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: 22
year: '2017'
...
---
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abstract:
- lang: eng
text: We prove the universality for the eigenvalue gap statistics in the bulk of
the spectrum for band matrices, in the regime where the band width is comparable
with the dimension of the matrix, W ~ N. All previous results concerning universality
of non-Gaussian random matrices are for mean-field models. By relying on a new
mean-field reduction technique, we deduce universality from quantum unique ergodicity
for band matrices.
article_processing_charge: No
arxiv: 1
author:
- first_name: Paul
full_name: Bourgade, Paul
last_name: Bourgade
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng
last_name: Yau
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band
matrices. Advances in Theoretical and Mathematical Physics. 2017;21(3):739-800.
doi:10.4310/ATMP.2017.v21.n3.a5
apa: Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a
class of random band matrices. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a5
chicago: Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for
a Class of Random Band Matrices.” Advances in Theoretical and Mathematical
Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a5.
ieee: P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random
band matrices,” Advances in Theoretical and Mathematical Physics, vol.
21, no. 3. International Press, pp. 739–800, 2017.
ista: Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random
band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.
mla: Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.”
Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International
Press, 2017, pp. 739–800, doi:10.4310/ATMP.2017.v21.n3.a5.
short: P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical
Physics 21 (2017) 739–800.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-08-25T00:00:00Z
date_updated: 2025-09-18T09:52:57Z
day: '25'
department:
- _id: LaEr
doi: 10.4310/ATMP.2017.v21.n3.a5
ec_funded: 1
external_id:
arxiv:
- '1602.02312'
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isi: 1
issue: '3'
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- iso: eng
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url: https://arxiv.org/abs/1602.02312
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oa_version: Submitted Version
page: 739 - 800
project:
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call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- 1095-0761
publication_status: published
publisher: International Press
publist_id: '7337'
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title: Universality for a class of random band matrices
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volume: 21
year: '2017'
...
---
_id: '567'
abstract:
- lang: eng
text: "This book is a concise and self-contained introduction of recent techniques
to prove local spectral universality for large random matrices. Random matrix
theory is a fast expanding research area, and this book mainly focuses on the
methods that the authors participated in developing over the past few years. Many
other interesting topics are not included, and neither are several new developments
within the framework of these methods. The authors have chosen instead to present
key concepts that they believe are the core of these methods and should be relevant
for future applications. They keep technicalities to a minimum to make the book
accessible to graduate students. With this in mind, they include in this book
the basic notions and tools for high-dimensional analysis, such as large deviation,
entropy, Dirichlet form, and the logarithmic Sobolev inequality.\r\n"
alternative_title:
- Courant Lecture Notes
article_processing_charge: No
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng
last_name: Yau
citation:
ama: Erdös L, Yau H. A Dynamical Approach to Random Matrix Theory. Vol 28.
American Mathematical Society; 2017. doi:10.1090/cln/028
apa: Erdös, L., & Yau, H. (2017). A Dynamical Approach to Random Matrix Theory
(Vol. 28). American Mathematical Society. https://doi.org/10.1090/cln/028
chicago: Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix
Theory. Vol. 28. Courant Lecture Notes. American Mathematical Society, 2017.
https://doi.org/10.1090/cln/028.
ieee: L. Erdös and H. Yau, A Dynamical Approach to Random Matrix Theory,
vol. 28. American Mathematical Society, 2017.
ista: Erdös L, Yau H. 2017. A Dynamical Approach to Random Matrix Theory, American
Mathematical Society, 226p.
mla: Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory.
Vol. 28, American Mathematical Society, 2017, doi:10.1090/cln/028.
short: L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American
Mathematical Society, 2017.
corr_author: '1'
date_created: 2018-12-11T11:47:13Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2025-04-15T08:05:02Z
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department:
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doi: 10.1090/cln/028
ec_funded: 1
intvolume: ' 28'
language:
- iso: eng
month: '01'
oa_version: None
page: '226'
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication_identifier:
eisbn:
- 978-1-4704-4194-4
isbn:
- 9-781-4704-3648-3
publication_status: published
publisher: American Mathematical Society
publist_id: '7247'
quality_controlled: '1'
series_title: Courant Lecture Notes
status: public
title: A Dynamical Approach to Random Matrix Theory
type: book
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2017'
...