Almost-Hermitian random matrices and bandlimited point processes
(2023) In Analysis and Mathematical Physics 13(3).- Abstract
- We study the distribution of eigenvalues of almost-Hermitian random matrices associated with the classical Gaussian and Laguerre unitary ensembles. In the almost-Hermitian setting, which was pioneered by Fyodorov, Khoruzhenko and Sommers in the case of GUE, the eigenvalues are not confined to the real axis, but instead have imaginary parts which vary within a narrow “band” about the real line, of height proportional to 1/N, where N denotes the size of the matrices. We study vertical cross-sections of the 1-point density as well as microscopic scaling limits, and we compare with other results which have appeared in the literature in recent years. Our approach uses Ward’s equation and a property which we call “cross-section convergence”,... (More)
- We study the distribution of eigenvalues of almost-Hermitian random matrices associated with the classical Gaussian and Laguerre unitary ensembles. In the almost-Hermitian setting, which was pioneered by Fyodorov, Khoruzhenko and Sommers in the case of GUE, the eigenvalues are not confined to the real axis, but instead have imaginary parts which vary within a narrow “band” about the real line, of height proportional to 1/N, where N denotes the size of the matrices. We study vertical cross-sections of the 1-point density as well as microscopic scaling limits, and we compare with other results which have appeared in the literature in recent years. Our approach uses Ward’s equation and a property which we call “cross-section convergence”, which relates the large-N limit of the cross-sections of the density of eigenvalues with the equilibrium density for the corresponding Hermitian ensemble: the semi-circle law for GUE and the Marchenko–Pastur law for LUE. As an application of our approach, we prove the bulk universality of the almost-circular ensembles. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/256634cf-ab48-4f87-a4dd-b9db8d7f93f4
- author
- Ameur, Yacin LU and Byun, Sung-Soo
- organization
- publishing date
- 2023-05-30
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Almost-Hermitian GUE/LUE, Bandlimited Coulomb gas, Cross-section convergence, Ward’s equation, Translation invariance
- in
- Analysis and Mathematical Physics
- volume
- 13
- issue
- 3
- article number
- 52
- pages
- 57 pages
- publisher
- Springer
- external identifiers
-
- scopus:85160623787
- ISSN
- 1664-2368
- DOI
- 10.1007/s13324-023-00808-8
- language
- English
- LU publication?
- yes
- id
- 256634cf-ab48-4f87-a4dd-b9db8d7f93f4
- alternative location
- https://doi.org/10.1007/s13324-023-00808-8
- date added to LUP
- 2023-06-12 11:54:00
- date last changed
- 2023-06-13 04:02:30
@article{256634cf-ab48-4f87-a4dd-b9db8d7f93f4,
abstract = {{We study the distribution of eigenvalues of almost-Hermitian random matrices associated with the classical Gaussian and Laguerre unitary ensembles. In the almost-Hermitian setting, which was pioneered by Fyodorov, Khoruzhenko and Sommers in the case of GUE, the eigenvalues are not confined to the real axis, but instead have imaginary parts which vary within a narrow “band” about the real line, of height proportional to 1/N, where N denotes the size of the matrices. We study vertical cross-sections of the 1-point density as well as microscopic scaling limits, and we compare with other results which have appeared in the literature in recent years. Our approach uses Ward’s equation and a property which we call “cross-section convergence”, which relates the large-N limit of the cross-sections of the density of eigenvalues with the equilibrium density for the corresponding Hermitian ensemble: the semi-circle law for GUE and the Marchenko–Pastur law for LUE. As an application of our approach, we prove the bulk universality of the almost-circular ensembles.}},
author = {{Ameur, Yacin and Byun, Sung-Soo}},
issn = {{1664-2368}},
keywords = {{Almost-Hermitian GUE/LUE; Bandlimited Coulomb gas; Cross-section convergence; Ward’s equation; Translation invariance}},
language = {{eng}},
month = {{05}},
number = {{3}},
publisher = {{Springer}},
series = {{Analysis and Mathematical Physics}},
title = {{Almost-Hermitian random matrices and bandlimited point processes}},
url = {{http://dx.doi.org/10.1007/s13324-023-00808-8}},
doi = {{10.1007/s13324-023-00808-8}},
volume = {{13}},
year = {{2023}},
}