---
_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
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'
...