---
_id: '6511'
abstract:
- lang: eng
text: Let U and V be two independent N by N random matrices that are distributed
according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N
matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts
that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly,
in the limit of large N, to a deterministic measure which is supported on a single
ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior
of the single ring, we establish the convergence of the empirical eigenvalue distribution
on the optimal local scale of order N−1/2+ε and establish the optimal convergence
rate. The same results hold true when U and V are Haar distributed on O(N).
article_processing_charge: No
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. Local single ring theorem on optimal scale. Annals
of Probability. 2019;47(3):1270-1334. doi:10.1214/18-AOP1284
apa: Bao, Z., Erdös, L., & Schnelli, K. (2019). Local single ring theorem on
optimal scale. Annals of Probability. Institute of Mathematical Statistics.
https://doi.org/10.1214/18-AOP1284
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem
on Optimal Scale.” Annals of Probability. Institute of Mathematical Statistics,
2019. https://doi.org/10.1214/18-AOP1284.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,”
Annals of Probability, vol. 47, no. 3. Institute of Mathematical Statistics,
pp. 1270–1334, 2019.
ista: Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale.
Annals of Probability. 47(3), 1270–1334.
mla: Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” Annals
of Probability, vol. 47, no. 3, Institute of Mathematical Statistics, 2019,
pp. 1270–334, doi:10.1214/18-AOP1284.
short: Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.
date_created: 2019-06-02T21:59:13Z
date_published: 2019-05-01T00:00:00Z
date_updated: 2025-07-10T11:53:28Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/18-AOP1284
ec_funded: 1
external_id:
arxiv:
- '1612.05920'
isi:
- '000466616100003'
intvolume: ' 47'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1612.05920
month: '05'
oa: 1
oa_version: Preprint
page: 1270-1334
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'
scopus_import: '1'
status: public
title: Local single ring theorem on optimal scale
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 47
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: 2025-07-10T11:53:55Z
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:
- 1096-0813
issn:
- 0022-247X
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 480
year: '2019'
...
---
OA_place: repository
OA_type: green
_id: '7035'
abstract:
- lang: eng
text: 'The aim of this short note is to expound one particular issue that was discussed
during the talk [10] given at the symposium ”Researches on isometries as preserver
problems and related topics” at Kyoto RIMS. That is, the role of Dirac masses
by describing the isometry group of various metric spaces of probability measures. This article is of survey character, and it does not contain any essentially new
results.From an isometric point of view, in some cases, metric spaces of measures
are similar to C(K)-type function spaces. Similarity means here that their isometries are driven by some nice transformations
of the underlying space. Of course, it depends on the particular choice of the metric how nice these
transformations should be. Sometimes, as we will see, being a homeomorphism is
enough to generate an isometry. But sometimes we need more: the transformation
must preserve the underlying distance as well. Statements claiming that isometries
in questions are necessarily induced by homeomorphisms are called Banach-Stone-type
results, while results asserting that the underlying transformation is necessarily
an isometry are termed as isometric rigidity results.As Dirac masses can be considered as building bricks of the set of all Borel measures, a natural
question arises:Is it enough to understand how an isometry acts on the set of
Dirac masses? Does this action extend uniquely to all measures?In what follows,
we will thoroughly investigate this question.'
acknowledgement: "This paper is part of a long term collaboration investigating the
isometric structure of Wasserstein\r\nspaces. The authors would like to thank the
warm hospitality and generosity of László Erdós and his\r\ngroup at Institute of
Science and Technology Austria.\r\nT. Titkos wants to thank Oriental Business and
Innovation Center ‐ OBIC for providing financial\r\nsupport to participate in the
symposium at the Kyoto RIMS.\r\nGy. P. Gehér was supported by the Leverhulme Trust
Early Career Fellowship (ECF‐2018‐125),\r\nand also by the Hungarian National Research,
Development and Innovation Office (K115383). T.\r\nTitkos was supported by the Hungarian
National Research, Development and Innovation Office‐ NKFIH\r\n(PD128374), by the
János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the\r\nUNKP‐18‐4‐BGE‐3
New National Excellence Program of the Ministry of Human Capacities. D. Virosztek\r\nwas
supported by the ISTFELLOW program of the Institute of Science and Technology Austria
(project\r\ncode IC1027FELL01 ) and partially supported by the Hungarian National
Research, Development and\r\nInnovation Office NKFIH (grant no. K124152 and grant
no. KH129601)"
article_processing_charge: No
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. Dirac masses and isometric rigidity. In:
Kyoto RIMS Kôkyûroku. Vol 2125. Research Institute for Mathematical Sciences,
Kyoto University; 2019:34-41.'
apa: 'Geher, G. P., Titkos, T., & Virosztek, D. (2019). Dirac masses and isometric
rigidity. In Kyoto RIMS Kôkyûroku (Vol. 2125, pp. 34–41). Kyoto, Japan:
Research Institute for Mathematical Sciences, Kyoto University.'
chicago: Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Dirac Masses and
Isometric Rigidity.” In Kyoto RIMS Kôkyûroku, 2125:34–41. Research Institute
for Mathematical Sciences, Kyoto University, 2019.
ieee: G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,”
in Kyoto RIMS Kôkyûroku, Kyoto, Japan, 2019, vol. 2125, pp. 34–41.
ista: Geher GP, Titkos T, Virosztek D. 2019. Dirac masses and isometric rigidity.
Kyoto RIMS Kôkyûroku. Research on isometries as preserver problems and related
topics vol. 2125, 34–41.
mla: Geher, Gyorgy Pal, et al. “Dirac Masses and Isometric Rigidity.” Kyoto RIMS
Kôkyûroku, vol. 2125, Research Institute for Mathematical Sciences, Kyoto
University, 2019, pp. 34–41.
short: G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research
Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.
conference:
end_date: 2019-01-30
location: Kyoto, Japan
name: Research on isometries as preserver problems and related topics
start_date: 2019-01-28
corr_author: '1'
date_created: 2019-11-18T15:39:53Z
date_published: 2019-01-30T00:00:00Z
date_updated: 2025-06-30T09:55:30Z
day: '30'
department:
- _id: LaEr
ec_funded: 1
intvolume: ' 2125'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html
month: '01'
oa: 1
oa_version: Submitted Version
page: 34-41
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Kyoto RIMS Kôkyûroku
publication_status: published
publisher: Research Institute for Mathematical Sciences, Kyoto University
quality_controlled: '1'
status: public
title: Dirac masses and isometric rigidity
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2125
year: '2019'
...
---
_id: '72'
abstract:
- lang: eng
text: We consider the totally asymmetric simple exclusion process (TASEP) with non-random
initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle
initially at the origin. For ρ<λ, there is a shock and the second class particle
moves with speed 1−λ−ρ. For large time t, we show that the position of the second
class particle fluctuates on a t1/3 scale and determine its limiting law. We also
obtain the limiting distribution of the number of steps made by the second class
particle until time t.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Patrick
full_name: Ferrari, Patrick
last_name: Ferrari
- first_name: Promit
full_name: Ghosal, Promit
last_name: Ghosal
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
citation:
ama: Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP
with non-random initial condition. Annales de l’institut Henri Poincare (B)
Probability and Statistics. 2019;55(3):1203-1225. doi:10.1214/18-AIHP916
apa: Ferrari, P., Ghosal, P., & Nejjar, P. (2019). Limit law of a second class
particle in TASEP with non-random initial condition. Annales de l’institut
Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics.
https://doi.org/10.1214/18-AIHP916
chicago: Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second
Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut
Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics,
2019. https://doi.org/10.1214/18-AIHP916.
ieee: P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle
in TASEP with non-random initial condition,” Annales de l’institut Henri Poincare
(B) Probability and Statistics, vol. 55, no. 3. Institute of Mathematical
Statistics, pp. 1203–1225, 2019.
ista: Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle
in TASEP with non-random initial condition. Annales de l’institut Henri Poincare
(B) Probability and Statistics. 55(3), 1203–1225.
mla: Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with
Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability
and Statistics, vol. 55, no. 3, Institute of Mathematical Statistics, 2019,
pp. 1203–25, doi:10.1214/18-AIHP916.
short: P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B)
Probability and Statistics 55 (2019) 1203–1225.
date_created: 2018-12-11T11:44:29Z
date_published: 2019-09-25T00:00:00Z
date_updated: 2025-04-14T07:27:49Z
day: '25'
department:
- _id: LaEr
- _id: JaMa
doi: 10.1214/18-AIHP916
ec_funded: 1
external_id:
arxiv:
- '1710.02323'
isi:
- '000487763200001'
intvolume: ' 55'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1710.02323
month: '09'
oa: 1
oa_version: Preprint
page: 1203-1225
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 de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Limit law of a second class particle in TASEP with non-random initial condition
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2019'
...
---
_id: '7423'
abstract:
- lang: eng
text: 'We compare finite rank perturbations of the following three ensembles of
complex rectangular random matrices: First, a generalised Wishart ensemble with
one random and two fixed correlation matrices introduced by Borodin and Péché,
second, the product of two independent random matrices where one has correlated
entries, and third, the case when the two random matrices become also coupled
through a fixed matrix. The singular value statistics of all three ensembles is
shown to be determinantal and we derive double contour integral representations
for their respective kernels. Three different kernels are found in the limit of
infinite matrix dimension at the origin of the spectrum. They depend on finite
rank perturbations of the correlation and coupling matrices and are shown to be
integrable. The first kernel (I) is found for two independent matrices from the
second, and two weakly coupled matrices from the third ensemble. It generalises
the Meijer G-kernel for two independent and uncorrelated matrices. The third kernel
(III) is obtained for the generalised Wishart ensemble and for two strongly coupled
matrices. It further generalises the perturbed Bessel kernel of Desrosiers and
Forrester. Finally, kernel (II), found for the ensemble of two coupled matrices,
provides an interpolation between the kernels (I) and (III), generalising previous
findings of part of the authors.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gernot
full_name: Akemann, Gernot
last_name: Akemann
- first_name: Tomasz
full_name: Checinski, Tomasz
last_name: Checinski
- first_name: Dangzheng
full_name: Liu, Dangzheng
id: 2F947E34-F248-11E8-B48F-1D18A9856A87
last_name: Liu
- first_name: Eugene
full_name: Strahov, Eugene
last_name: Strahov
citation:
ama: 'Akemann G, Checinski T, Liu D, Strahov E. Finite rank perturbations in products
of coupled random matrices: From one correlated to two Wishart ensembles. Annales
de l’Institut Henri Poincaré, Probabilités et Statistiques. 2019;55(1):441-479.
doi:10.1214/18-aihp888'
apa: 'Akemann, G., Checinski, T., Liu, D., & Strahov, E. (2019). Finite rank
perturbations in products of coupled random matrices: From one correlated to two
Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques.
Institute of Mathematical Statistics. https://doi.org/10.1214/18-aihp888'
chicago: 'Akemann, Gernot, Tomasz Checinski, Dangzheng Liu, and Eugene Strahov.
“Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated
to Two Wishart Ensembles.” Annales de l’Institut Henri Poincaré, Probabilités
et Statistiques. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-aihp888.'
ieee: 'G. Akemann, T. Checinski, D. Liu, and E. Strahov, “Finite rank perturbations
in products of coupled random matrices: From one correlated to two Wishart ensembles,”
Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol.
55, no. 1. Institute of Mathematical Statistics, pp. 441–479, 2019.'
ista: 'Akemann G, Checinski T, Liu D, Strahov E. 2019. Finite rank perturbations
in products of coupled random matrices: From one correlated to two Wishart ensembles.
Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 55(1), 441–479.'
mla: 'Akemann, Gernot, et al. “Finite Rank Perturbations in Products of Coupled
Random Matrices: From One Correlated to Two Wishart Ensembles.” Annales de
l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1, Institute
of Mathematical Statistics, 2019, pp. 441–79, doi:10.1214/18-aihp888.'
short: G. Akemann, T. Checinski, D. Liu, E. Strahov, Annales de l’Institut Henri
Poincaré, Probabilités et Statistiques 55 (2019) 441–479.
date_created: 2020-01-30T10:36:50Z
date_published: 2019-02-01T00:00:00Z
date_updated: 2023-09-06T14:58:39Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/18-aihp888
external_id:
arxiv:
- '1704.05224'
isi:
- '000456070200013'
intvolume: ' 55'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1704.05224
month: '02'
oa: 1
oa_version: Preprint
page: 441-479
publication: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
status: public
title: 'Finite rank perturbations in products of coupled random matrices: From one
correlated to two Wishart ensembles'
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 55
year: '2019'
...
---
_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'
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date_updated: 2020-07-14T12:46:26Z
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file_size: 1201840
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intvolume: ' 173'
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issue: 1-2
language:
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month: '02'
oa: 1
oa_version: Published Version
page: 293–373
project:
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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
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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:
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- 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
file_size: 394851
relation: main_file
file_date_updated: 2020-07-14T12:47:46Z
has_accepted_license: '1'
intvolume: ' 15'
isi: 1
issue: '2'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1311-1334
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: 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
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oa_version: Preprint
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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
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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:
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date_created: 2019-04-08T13:55:20Z
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language:
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month: '07'
oa: 1
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:
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status: public
scopus_import: '1'
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title: Local inhomogeneous circular law
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 28
year: '2018'
...