Translator Disclaimer
1 June 2006 Painlevé formulas of the limiting distributions for nonnull complex sample covariance matrices
Jinho Baik
Author Affiliations +
Duke Math. J. 133(2): 205-235 (1 June 2006). DOI: 10.1215/S0012-7094-06-13321-5

Abstract

In a recent study of large nonnull sample covariance matrices, a new sequence of functions generalizing the Gaussian unitary ensemble (GUE) Tracy-Widom distribution of random matrix theory was obtained. This article derives Painlevé formulas of these functions and uses them to prove that they are indeed distribution functions. Applications of these new distribution functions to last-passage percolation, queues in tandem, and totally asymmetric simple exclusion process are also discussed. As a part of the proof, a representation of orthogonal polynomials on the unit circle in terms of an operator on a discrete set is presented

Citation

Download Citation

Jinho Baik. "Painlevé formulas of the limiting distributions for nonnull complex sample covariance matrices." Duke Math. J. 133 (2) 205 - 235, 1 June 2006. https://doi.org/10.1215/S0012-7094-06-13321-5

Information

Published: 1 June 2006
First available in Project Euclid: 21 May 2006

zbMATH: 1139.33006
MathSciNet: MR2225691
Digital Object Identifier: 10.1215/S0012-7094-06-13321-5

Subjects:
Primary: 33E17, 60E99, 62E99

Rights: Copyright © 2006 Duke University Press

JOURNAL ARTICLE
31 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.133 • No. 2 • 1 June 2006
Back to Top