Download this article
Download this article For screen
For printing
Recent Issues
Volume 5, Issue 4
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
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 2690-1005 (online)
ISSN 2690-0998 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Airy point process via supersymmetric lifts

Andrew Ahn

Vol. 3 (2022), No. 4, 869–938
Abstract

We study the local asymptotics at the edge for particle systems arising either from eigenvalues of sums of unitarily invariant random Hermitian matrices or from signatures corresponding to decompositions of tensor products of representations of the unitary group. Our method treats these two models in parallel, and is based on new formulas for observables described in terms of a special family of lifts, which we call supersymmetric lifts, of Schur functions and multivariate Bessel functions. We obtain explicit expressions for a class of supersymmetric lifts inspired by determinantal formulas for supersymmetric Schur functions due to Moens and Van der Jeugt (J. Algebraic Combin. 17:3 (2003), 283–307). Asymptotic analysis of these lifts enable us to probe the edge. We focus on several settings where the Airy point process arises.

PDF Access Denied

We have not been able to recognize your IP address 18.97.14.83 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
free convolution, random matrices, Airy point process, quantized free convolution
Mathematical Subject Classification
Primary: 60B15, 60B20
Secondary: 22E46
Milestones
Received: 12 October 2021
Accepted: 6 June 2022
Published: 21 February 2023
Authors
Andrew Ahn
Cornell University
Ithaca, NY
United States