On the almost-circular symplectic induced Ginibre ensemble
(2023) In Studies in Applied Mathematics 150(1). p.184-217- Abstract
We consider the symplectic-induced Ginibre process, which is a Pfaffian point process on the plane. Let N be the number of points. We focus on the almost-circular regime where most of the points lie in a thin annulus (Formula presented.) of width (Formula presented.) as (Formula presented.). Our main results are the bulk scaling limits of all correlation functions near the real axis, and also away from the real axis. Near the real axis, the limiting correlation functions are Pfaffians with a new correlation kernel, which interpolates the limiting kernels in the bulk of the symplectic Ginibre ensemble and of the antisymmetric Gaussian Hermitian ensemble of odd size. Away from the real axis, the limiting correlation functions are... (More)
We consider the symplectic-induced Ginibre process, which is a Pfaffian point process on the plane. Let N be the number of points. We focus on the almost-circular regime where most of the points lie in a thin annulus (Formula presented.) of width (Formula presented.) as (Formula presented.). Our main results are the bulk scaling limits of all correlation functions near the real axis, and also away from the real axis. Near the real axis, the limiting correlation functions are Pfaffians with a new correlation kernel, which interpolates the limiting kernels in the bulk of the symplectic Ginibre ensemble and of the antisymmetric Gaussian Hermitian ensemble of odd size. Away from the real axis, the limiting correlation functions are determinants, and the kernel is the same as the one appearing in the bulk limit of almost-Hermitian random matrices. Furthermore, we obtain precise large N asymptotics for the probability that no points lie outside (Formula presented.), as well as of several other “semi-large” gap probabilities.
(Less)
- author
- Byun, Sung Soo and Charlier, Christophe LU
- organization
- publishing date
- 2023-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- asymptotic analysis, random matrix theory, universality
- in
- Studies in Applied Mathematics
- volume
- 150
- issue
- 1
- pages
- 34 pages
- publisher
- Wiley-Blackwell
- external identifiers
-
- scopus:85142417500
- ISSN
- 0022-2526
- DOI
- 10.1111/sapm.12537
- language
- English
- LU publication?
- yes
- id
- f57a0a65-ce76-4334-8509-6d70560a6e79
- date added to LUP
- 2023-01-26 15:32:55
- date last changed
- 2023-01-26 15:32:55
@article{f57a0a65-ce76-4334-8509-6d70560a6e79,
abstract = {{<p>We consider the symplectic-induced Ginibre process, which is a Pfaffian point process on the plane. Let N be the number of points. We focus on the almost-circular regime where most of the points lie in a thin annulus (Formula presented.) of width (Formula presented.) as (Formula presented.). Our main results are the bulk scaling limits of all correlation functions near the real axis, and also away from the real axis. Near the real axis, the limiting correlation functions are Pfaffians with a new correlation kernel, which interpolates the limiting kernels in the bulk of the symplectic Ginibre ensemble and of the antisymmetric Gaussian Hermitian ensemble of odd size. Away from the real axis, the limiting correlation functions are determinants, and the kernel is the same as the one appearing in the bulk limit of almost-Hermitian random matrices. Furthermore, we obtain precise large N asymptotics for the probability that no points lie outside (Formula presented.), as well as of several other “semi-large” gap probabilities.</p>}},
author = {{Byun, Sung Soo and Charlier, Christophe}},
issn = {{0022-2526}},
keywords = {{asymptotic analysis; random matrix theory; universality}},
language = {{eng}},
number = {{1}},
pages = {{184--217}},
publisher = {{Wiley-Blackwell}},
series = {{Studies in Applied Mathematics}},
title = {{On the almost-circular symplectic induced Ginibre ensemble}},
url = {{http://dx.doi.org/10.1111/sapm.12537}},
doi = {{10.1111/sapm.12537}},
volume = {{150}},
year = {{2023}},
}