---
_id: '6086'
abstract:
- lang: eng
text: We show that linear analytic cocycles where all Lyapunov exponents are negative
infinite are nilpotent. For such one-frequency cocycles we show that they can
be analytically conjugated to an upper triangular cocycle or a Jordan normal form.
As a consequence, an arbitrarily small analytic perturbation leads to distinct
Lyapunov exponents. Moreover, in the one-frequency case where the th Lyapunov
exponent is finite and the st negative infinite, we obtain a simple criterion
for domination in which case there is a splitting into a nilpotent part and an
invertible part.
article_processing_charge: No
arxiv: 1
author:
- first_name: Christian
full_name: Sadel, Christian
id: 4760E9F8-F248-11E8-B48F-1D18A9856A87
last_name: Sadel
orcid: 0000-0001-8255-3968
- first_name: Disheng
full_name: Xu, Disheng
last_name: Xu
citation:
ama: Sadel C, Xu D. Singular analytic linear cocycles with negative infinite Lyapunov
exponents. Ergodic Theory and Dynamical Systems. 2019;39(4):1082-1098.
doi:10.1017/etds.2017.52
apa: Sadel, C., & Xu, D. (2019). Singular analytic linear cocycles with negative
infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. Cambridge
University Press. https://doi.org/10.1017/etds.2017.52
chicago: Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with
Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems.
Cambridge University Press, 2019. https://doi.org/10.1017/etds.2017.52.
ieee: C. Sadel and D. Xu, “Singular analytic linear cocycles with negative infinite
Lyapunov exponents,” Ergodic Theory and Dynamical Systems, vol. 39, no.
4. Cambridge University Press, pp. 1082–1098, 2019.
ista: Sadel C, Xu D. 2019. Singular analytic linear cocycles with negative infinite
Lyapunov exponents. Ergodic Theory and Dynamical Systems. 39(4), 1082–1098.
mla: Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative
Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems, vol.
39, no. 4, Cambridge University Press, 2019, pp. 1082–98, doi:10.1017/etds.2017.52.
short: C. Sadel, D. Xu, Ergodic Theory and Dynamical Systems 39 (2019) 1082–1098.
date_created: 2019-03-10T22:59:18Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2025-04-15T06:50:24Z
day: '01'
department:
- _id: LaEr
doi: 10.1017/etds.2017.52
ec_funded: 1
external_id:
arxiv:
- '1601.06118'
isi:
- '000459725600012'
intvolume: ' 39'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1601.06118
month: '04'
oa: 1
oa_version: Preprint
page: 1082-1098
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Ergodic Theory and Dynamical Systems
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Singular analytic linear cocycles with negative infinite Lyapunov exponents
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 39
year: '2019'
...
---
_id: '8175'
abstract:
- lang: eng
text: We study edge asymptotics of poissonized Plancherel-type measures on skew
Young diagrams (integer partitions). These measures can be seen as generalizations
of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's
problem on longest increasing subsequences of random permutations and the last
passage percolation (corner growth) discrete versions thereof. Moreover they interpolate
between said measures and the uniform measure on partitions. In the new KPZ-like
1/3 exponent edge scaling limit with logarithmic corrections, we find new probability
distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions
from the theory of random matrices.
acknowledgement: "D.B. is especially grateful to Patrik Ferrari for suggesting simplifications
in Section 3 and\r\nto Alessandra Occelli for suggesting the name for the models
of Section 2.\r\n"
article_number: '34'
article_processing_charge: No
arxiv: 1
author:
- first_name: Dan
full_name: Betea, Dan
last_name: Betea
- first_name: Jérémie
full_name: Bouttier, Jérémie
last_name: Bouttier
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
- first_name: Mirjana
full_name: Vuletíc, Mirjana
last_name: Vuletíc
citation:
ama: 'Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young
diagrams via free boundaries. In: Proceedings on the 31st International Conference
on Formal Power Series and Algebraic Combinatorics. Formal Power Series and
Algebraic Combinatorics; 2019.'
apa: 'Betea, D., Bouttier, J., Nejjar, P., & Vuletíc, M. (2019). New edge asymptotics
of skew Young diagrams via free boundaries. In Proceedings on the 31st International
Conference on Formal Power Series and Algebraic Combinatorics. Ljubljana,
Slovenia: Formal Power Series and Algebraic Combinatorics.'
chicago: Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge
Asymptotics of Skew Young Diagrams via Free Boundaries.” In Proceedings on
the 31st International Conference on Formal Power Series and Algebraic Combinatorics.
Formal Power Series and Algebraic Combinatorics, 2019.
ieee: D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of
skew Young diagrams via free boundaries,” in Proceedings on the 31st International
Conference on Formal Power Series and Algebraic Combinatorics, Ljubljana,
Slovenia, 2019.
ista: 'Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew
Young diagrams via free boundaries. Proceedings on the 31st International Conference
on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference
on Formal Power Series and Algebraic Combinatorics, 34.'
mla: Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.”
Proceedings on the 31st International Conference on Formal Power Series and
Algebraic Combinatorics, 34, Formal Power Series and Algebraic Combinatorics,
2019.
short: D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st
International Conference on Formal Power Series and Algebraic Combinatorics, Formal
Power Series and Algebraic Combinatorics, 2019.
conference:
end_date: 2019-07-05
location: Ljubljana, Slovenia
name: 'FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics'
start_date: 2019-07-01
date_created: 2020-07-26T22:01:04Z
date_published: 2019-07-01T00:00:00Z
date_updated: 2021-01-12T08:17:18Z
day: '01'
department:
- _id: LaEr
ec_funded: 1
external_id:
arxiv:
- '1902.08750'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.08750
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Proceedings on the 31st International Conference on Formal Power Series
and Algebraic Combinatorics
publication_status: published
publisher: Formal Power Series and Algebraic Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: New edge asymptotics of skew Young diagrams via free boundaries
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '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'
file:
- access_level: open_access
checksum: f9354fa5c71f9edd17132588f0dc7d01
content_type: application/pdf
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
relation: main_file
file_date_updated: 2020-07-14T12:46:26Z
has_accepted_license: '1'
intvolume: ' 173'
isi: 1
issue: 1-2
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
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'
...
---
_id: '10879'
abstract:
- lang: eng
text: We study effects of a bounded and compactly supported perturbation on multidimensional
continuum random Schrödinger operators in the region of complete localisation.
Our main emphasis is on Anderson orthogonality for random Schrödinger operators.
Among others, we prove that Anderson orthogonality does occur for Fermi energies
in the region of complete localisation with a non-zero probability. This partially
confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015),
560–565]. The spectral shift function plays an important role in our analysis
of Anderson orthogonality. We identify it with the index of the corresponding
pair of spectral projections and explore the consequences thereof. All our results
rely on the main technical estimate of this paper which guarantees separate exponential
decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b.
Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication
operator corresponding to the indicator function of a unit cube centred about
a∈Rd, and f is in a suitable class of functions of bounded variation with distributional
derivative supported in the region of complete localisation for H.
acknowledgement: M.G. was supported by the DFG under grant GE 2871/1-1.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Adrian M
full_name: Dietlein, Adrian M
id: 317CB464-F248-11E8-B48F-1D18A9856A87
last_name: Dietlein
- first_name: Martin
full_name: Gebert, Martin
last_name: Gebert
- first_name: Peter
full_name: Müller, Peter
last_name: Müller
citation:
ama: Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger
operators with applications to Anderson orthogonality and the spectral shift function.
Journal of Spectral Theory. 2019;9(3):921-965. doi:10.4171/jst/267
apa: Dietlein, A. M., Gebert, M., & Müller, P. (2019). Perturbations of continuum
random Schrödinger operators with applications to Anderson orthogonality and the
spectral shift function. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/jst/267
chicago: Dietlein, Adrian M, Martin Gebert, and Peter Müller. “Perturbations of
Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality
and the Spectral Shift Function.” Journal of Spectral Theory. EMS Press,
2019. https://doi.org/10.4171/jst/267.
ieee: A. M. Dietlein, M. Gebert, and P. Müller, “Perturbations of continuum random
Schrödinger operators with applications to Anderson orthogonality and the spectral
shift function,” Journal of Spectral Theory, vol. 9, no. 3. EMS Press,
pp. 921–965, 2019.
ista: Dietlein AM, Gebert M, Müller P. 2019. Perturbations of continuum random Schrödinger
operators with applications to Anderson orthogonality and the spectral shift function.
Journal of Spectral Theory. 9(3), 921–965.
mla: Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger
Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.”
Journal of Spectral Theory, vol. 9, no. 3, EMS Press, 2019, pp. 921–65,
doi:10.4171/jst/267.
short: A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019)
921–965.
das_tickbox: '1'
date_created: 2022-03-18T12:36:42Z
date_published: 2019-03-01T00:00:00Z
date_updated: 2026-07-06T11:54:18Z
day: '01'
department:
- _id: LaEr
doi: 10.4171/jst/267
external_id:
arxiv:
- '1701.02956'
isi:
- '000484709400006'
intvolume: ' 9'
isi: 1
issue: '3'
keyword:
- Random Schrödinger operators
- spectral shift function
- Anderson orthogonality
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1701.02956
month: '03'
oa: 1
oa_version: Preprint
page: 921-965
publication: Journal of Spectral Theory
publication_identifier:
issn:
- 1664-039X
publication_status: published
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Perturbations of continuum random Schrödinger operators with applications to
Anderson orthogonality and the spectral shift function
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9
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 Poincaré, Probabilités et Statistiques.
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 Poincaré,
Probabilités et Statistiques. 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
Poincaré, Probabilités et Statistiques. 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 Poincaré, Probabilités
et Statistiques, 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 Poincaré, Probabilités et Statistiques.
55(2), 661–696.
mla: Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.”
Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 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 Poincaré,
Probabilités et Statistiques 55 (2019) 661–696.
das_tickbox: '1'
date_created: 2019-04-08T14:05:04Z
date_published: 2019-05-01T00:00:00Z
date_updated: 2026-07-08T06:17:16Z
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 Poincaré, Probabilités et Statistiques
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'
...
---
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: 2026-07-29T13:46:20Z
day: '18'
ddc:
- '515'
- '519'
degree_awarded: PhD
department:
- _id: LaEr
- _id: GradSch
doi: 10.15479/AT:ISTA:th6179
doi_confirm: '1'
ec_funded: 1
file:
- access_level: closed
checksum: 6926f66f28079a81c4937e3764be00fc
content_type: application/x-gzip
creator: dernst
date_created: 2019-03-28T08:53:52Z
date_updated: 2020-07-14T12:47:21Z
file_id: '6180'
file_name: 2019_Schroeder_Thesis.tar.gz
file_size: 7104482
relation: source_file
- access_level: open_access
checksum: 7d0ebb8d1207e89768cdd497a5bf80fb
content_type: application/pdf
creator: dernst
date_created: 2019-03-28T08:53:52Z
date_updated: 2020-07-14T12:47:21Z
file_id: '6181'
file_name: 2019_Schroeder_Thesis.pdf
file_size: 4228794
relation: main_file
file_date_updated: 2020-07-14T12:47:21Z
has_accepted_license: '1'
language:
- iso: eng
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
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: 2026-07-29T13:46:19Z
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: 2026-07-29T13:46:19Z
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: '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: '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: '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: '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: '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.
das_tickbox: '1'
date_created: 2018-12-11T11:45:03Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2026-07-06T14:02:06Z
day: '01'
ddc:
- '500'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2018'
...