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
Large deviation principles via spherical integrals

Serban Belinschi, Alice Guionnet and Jiaoyang Huang

Vol. 3 (2022), No. 3, 543–625
Abstract

We develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical integrals obtained by Guionnet and Zeitouni (J. Funct. Anal. 188:2 (2002), 461–515; J. Funct. Anal. 216:1 (2004), 230–241). As examples, we obtain

  1. the large deviation principle for the empirical distribution of the diagonal entries of UBNU, for a sequence of N × N diagonal matrices BN and unitary or orthogonal Haar distributed matrices U,

  2. a large deviation upper bound for the empirical eigenvalue distribution of AN + UBNU, for two sequences of N × N diagonal matrices AN,BN, and their complementary lower bounds at measures which are described by the free product with amalgamation,

  3. a large deviation principle for the Kostka number KλNηN, for two sequences of partitions λN,ηN with at most N rows,

  4. a large deviation upper bound for the Littlewood–Richardson coefficients cλNηNκN, for three sequences of partitions λN,ηN,κN with at most N rows, and their complementary lower bounds at nice measures.

Keywords
large deviation principles, spherical integral, Littlewood–Richardson coefficients
Mathematical Subject Classification
Primary: 60B20, 60F10
Secondary: 05E05
Milestones
Received: 4 December 2020
Revised: 17 December 2021
Accepted: 14 March 2022
Published: 12 December 2022
Authors
Serban Belinschi
CNRS-Institute de Mathématiques de Toulouse
Toulouse
France
Alice Guionnet
Mathematics Department
ENS Lyon
Lyon
France
Jiaoyang Huang
Courant Institute of Mathematical Sciences
New York University
New York, NY
United States