CaltechAUTHORS
  A Caltech Library Service

Gaussian Fluctuation for the Number of Particles in Airy, Bessel, Sine, and Other Determinantal Random Point Fields

Soshnikov, Alexander B. (2000) Gaussian Fluctuation for the Number of Particles in Airy, Bessel, Sine, and Other Determinantal Random Point Fields. Journal of Statistical Physics, 100 (3-4). pp. 491-522. ISSN 0022-4715. https://resolver.caltech.edu/CaltechAUTHORS:20200115-090842391

[img] PDF - Submitted Version
See Usage Policy.

244Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20200115-090842391

Abstract

We prove the Central Limit Theorem (CLT) for the number of eigenvalues near the spectrum edge for certain Hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the Gaussian fluctuation of the number of particles in random point fields with determinantal correlation functions. As another corollary of the Costin–Lebowitz Theorem we prove the CLT for the empirical distribution function of the eigenvalues of random matrices from classical compact groups.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1023/a:1018672622921DOIArticle
https://rdcu.be/b0mflPublisherFree ReadCube access
https://arxiv.org/abs/math-ph/9907012arXivDiscussion Paper
Additional Information:© 2000 Plenum Publishing Corporation. Received December 13, 1999. It is a pleasure to thank Prof. Ya. Sinai, who drew my attention to the preprint of Costin-Lebowitz paper some time ago, and the organizers of the Special Session on Integrable Systems and Random Matrix Theory (AMS Meeting at Tucson, November 13-15, 1998) and the Introductory Workshop on Random Matrix Models (MSRI, Berkeley, January 19-23, 1999) for the opportunity to attend the meetings, where the idea of this paper has been finalized. The work was partially supported by the Euler stipend from the German Mathematical Society.
Funders:
Funding AgencyGrant Number
Deutsche Mathematiker-VereinigungUNSPECIFIED
Subject Keywords:Determinantal random point fields; central limit theorem; random matrices; Airy and Bessel kernels; classical compact groups
Issue or Number:3-4
Record Number:CaltechAUTHORS:20200115-090842391
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200115-090842391
Official Citation:Soshnikov, A.B. Gaussian Fluctuation for the Number of Particles in Airy, Bessel, Sine, and Other Determinantal Random Point Fields. Journal of Statistical Physics 100, 491–522 (2000) doi:10.1023/A:1018672622921
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100731
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:15 Jan 2020 17:50
Last Modified:15 Jan 2020 17:50

Repository Staff Only: item control page