---
_id: '14667'
abstract:
- lang: eng
text: 'For large dimensional non-Hermitian random matrices X with real or complex
independent, identically distributed, centered entries, we consider the fluctuations
of f (X) as a matrix where f is an analytic function around the spectrum of X.
We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits
Gaussian fluctuations as the matrix size grows to infinity, which consists of
two independent modes corresponding to the tracial and traceless parts of A. We
find a new formula for the variance of the traceless part that involves the Frobenius
norm of A and the L2-norm of f on the boundary of the limiting spectrum. '
- lang: fre
text: On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne
de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction
analytique sur un domaine qui contient le spectre de X. On prouve que, pour une
matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A
sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant
aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie
pour la variance de la composante de trace nulle, qui fait intervenir la norme
de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.
acknowledgement: "The first author was partially supported by ERC Advanced Grant “RMTBeyond”
No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond”
No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated
editor for carefully reading this paper and providing helpful comments that improved
the quality of the article. Also the authors would like to thank Peter Forrester
for pointing out the reference [12] that was absent in the previous version of the
manuscript."
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: Hong Chang
full_name: Ji, Hong Chang
id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
last_name: Ji
citation:
ama: Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. Annales
de l’institut Henri Poincare (B) Probability and Statistics. 2023;59(4):2083-2105.
doi:10.1214/22-AIHP1304
apa: Erdös, L., & Ji, H. C. (2023). Functional CLT for non-Hermitian random
matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics.
Institute of Mathematical Statistics. https://doi.org/10.1214/22-AIHP1304
chicago: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics.
Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AIHP1304.
ieee: L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,”
Annales de l’institut Henri Poincare (B) Probability and Statistics, vol.
59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.
ista: Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales
de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.
mla: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics,
vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:10.1214/22-AIHP1304.
short: L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and
Statistics 59 (2023) 2083–2105.
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2023-12-11T12:36:56Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-AIHP1304
ec_funded: 1
external_id:
arxiv:
- '2112.11382'
intvolume: ' 59'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2112.11382
month: '11'
oa: 1
oa_version: Preprint
page: 2083-2105
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
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: Functional CLT for non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 59
year: '2023'
...
---
_id: '10797'
abstract:
- lang: eng
text: We consider symmetric partial exclusion and inclusion processes in a general
graph in contact with reservoirs, where we allow both for edge disorder and well-chosen
site disorder. We extend the classical dualities to this context and then we derive
new orthogonal polynomial dualities. From the classical dualities, we derive the
uniqueness of the non-equilibrium steady state and obtain correlation inequalities.
Starting from the orthogonal polynomial dualities, we show universal properties
of n-point correlation functions in the non-equilibrium steady state for systems
with at most two different reservoir parameters, such as a chain with reservoirs
at left and right ends.
- lang: fre
text: Nous considérons des processus d’exclusion partielle, et des processus d’inclusion
sur un graphe général en contact avec des réservoirs. Nous autorisons la présence
de inhomogenéités sur les arrêts ainsi que sur les sommets du graph. Nous généralisons
les “dualités classiques” dans ce contexte et nous démontrons des nouvelles dualités
orthogonales. À partir des dualités classiques, nous démontrons l’unicité de l’état
stationnaire non-équilibre, ainsi que des inégalités de corrélation. À partir
des dualités orthogonales nous démontrons des propriétés universelles des fonctions
de corrélation à n points dans l’état stationnaire non-équilibre pour des systèmes
avec deux paramètres de réservoirs inégaux, comme par exemple une chaîne avec
des réservoirs à droite et à gauche.
acknowledgement: The authors would like to thank Gioia Carinci and Cristian Giardinà
for useful discussions. F.R. and S.F. thank Jean-René Chazottes for a stay at CPHT
(Institut Polytechnique de Paris), in the realm of Chaire d’Alembert (Paris-Saclay
University), where part of this work was performed. S.F. acknowledges Simona Villa
for her support in creating the picture. S.F. acknowledges financial support from
NWO via the grant TOP1.17.019. F.S. acknowledges financial support from the European
Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie
grant agreement No. 754411.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Simone
full_name: Floreani, Simone
last_name: Floreani
- first_name: Frank
full_name: Redig, Frank
last_name: Redig
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: Floreani S, Redig F, Sau F. Orthogonal polynomial duality of boundary driven
particle systems and non-equilibrium correlations. Annales de l’institut Henri
Poincare (B) Probability and Statistics. 2022;58(1):220-247. doi:10.1214/21-AIHP1163
apa: Floreani, S., Redig, F., & Sau, F. (2022). Orthogonal polynomial duality
of boundary driven particle systems and non-equilibrium correlations. Annales
de l’institut Henri Poincare (B) Probability and Statistics. Institute of
Mathematical Statistics. https://doi.org/10.1214/21-AIHP1163
chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Orthogonal Polynomial
Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.”
Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute
of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AIHP1163.
ieee: S. Floreani, F. Redig, and F. Sau, “Orthogonal polynomial duality of boundary
driven particle systems and non-equilibrium correlations,” Annales de l’institut
Henri Poincare (B) Probability and Statistics, vol. 58, no. 1. Institute of
Mathematical Statistics, pp. 220–247, 2022.
ista: Floreani S, Redig F, Sau F. 2022. Orthogonal polynomial duality of boundary
driven particle systems and non-equilibrium correlations. Annales de l’institut
Henri Poincare (B) Probability and Statistics. 58(1), 220–247.
mla: Floreani, Simone, et al. “Orthogonal Polynomial Duality of Boundary Driven
Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri
Poincare (B) Probability and Statistics, vol. 58, no. 1, Institute of Mathematical
Statistics, 2022, pp. 220–47, doi:10.1214/21-AIHP1163.
short: S. Floreani, F. Redig, F. Sau, Annales de l’institut Henri Poincare (B) Probability
and Statistics 58 (2022) 220–247.
date_created: 2022-02-27T23:01:50Z
date_published: 2022-02-01T00:00:00Z
date_updated: 2023-10-17T12:49:43Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/21-AIHP1163
ec_funded: 1
external_id:
arxiv:
- '2007.08272'
isi:
- '000752489300010'
intvolume: ' 58'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2007.08272
month: '02'
oa: 1
oa_version: Preprint
page: 220-247
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium
correlations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2022'
...
---
_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: 2023-10-17T08:53:45Z
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: '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: 2023-10-17T12:20:20Z
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'
...