Journal article

Applications in random matrix theory of a PIII’ τ-function sequence from Okamoto’s Hamiltonian formulation

Dan Dai, Peter J Forrester, Shuai-Xia Xu

Random Matrices: Theory and Applications | World Scientific Pub Co Pte Lt

Abstract

We consider the singular linear statistic of the Laguerre unitary ensemble (LUE) consisting of the sum of the reciprocal of the eigenvalues. It is observed that the exponential generating function for this statistic can be written as a Toeplitz determinant with entries given in terms of particular [Formula: see text] Bessel functions. Earlier studies have identified the same determinant, but with the [Formula: see text] Bessel functions replaced by [Formula: see text] Bessel functions, as relating to the hard edge scaling limit of a generalized gap probability for the LUE, in the case of non-negative integer Laguerre parameter. We show that the Toeplitz determinant formed from an arbitrary l..

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University of Melbourne Researchers