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

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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:

URL	URL Type	Description
https://doi.org/10.1023/a:1018672622921	DOI	Article
https://rdcu.be/b0mfl	Publisher	Free ReadCube access
https://arxiv.org/abs/math-ph/9907012	arXiv	Discussion 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 Agency	Grant Number
Deutsche Mathematiker-Vereinigung	UNSPECIFIED

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

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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

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