Journal article

Finite-size corrections at the hard edge for the Laguerre beta ensemble

Peter J Forrester, Allan K Trinh

STUDIES IN APPLIED MATHEMATICS | WILEY | Published : 2019

Abstract

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight (Formula presented.), (Formula presented.) in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable (Formula presented.). Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that (Formula presented.). We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, ..

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University of Melbourne Researchers