Vol. 2, No. 2, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2690-1005
ISSN (print): 2690-0998
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Global rigidity and exponential moments for soft and hard edge point processes

Christophe Charlier and Tom Claeys

Vol. 2 (2021), No. 2, 363–417
Abstract

We establish global rigidity upper bounds for universal determinantal point processes describing edge eigenvalues of random matrices. For this, we first obtain a general result which can be applied to general (not necessarily determinantal) point processes which have a smallest (or largest) point: this allows us to deduce global rigidity upper bounds from the exponential moments of the counting function of the process. Combining our general result with known exponential moment asymptotics for the Airy and Bessel point processes, we improve on the best known upper bounds for the global rigidity of the Airy point process, and we obtain new global rigidity results for the Bessel point process.

Secondly, we obtain exponential moment asymptotics for Wright’s generalized Bessel process and the Meijer- G process, up to and including the constant term. As a direct consequence, we obtain new results for the expectation and variance of the associated counting functions. Furthermore, by combining these asymptotics with our general rigidity theorem, we obtain new global rigidity upper bounds for these point processes.

PDF Access Denied

We have not been able to recognize your IP address 44.222.104.206 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
rigidity, exponential moments, Muttalib–Borodin ensembles, product random matrices, random matrix theory, Asymptotic analysis, large gap probability, Riemann–Hilbert problems
Mathematical Subject Classification
Primary: 33B15, 33E20, 35Q15, 41A60, 60B20
Milestones
Received: 7 October 2020
Revised: 1 December 2020
Accepted: 15 December 2020
Published: 22 May 2021
Authors
Christophe Charlier
KTH Stockholm
Stockholm
Sweden
Tom Claeys
Institut de Recherche en Mathématique et Physique
UC Louvain
Louvain-La-Neuve
Belgium