Computable structural formulas for the distribution of the $\beta$-Jacobi edge eigenvalues
Abstract
The Jacobi ensemble is one of the classical ensembles of random matrix theory. Prominent in applications are properties of the eigenvalues at the spectrum edge, specifically the distribution of the largest (e.g. Roy's largest root test in multivariate statistics) and smallest (e.g.~condition numbers of linear systems) eigenvalues. We identify three ranges of parameter values for which the gap probability determining these distributions is a finite sum with respect to particular bases, and moreover make use of a certain differential-difference system fundamental in the theory of the Selberg integral to provide a recursive scheme to compute the corresponding coefficients.
Cite
@article{arxiv.2006.02238,
title = {Computable structural formulas for the distribution of the $\beta$-Jacobi edge eigenvalues},
author = {Peter J. Forrester and Santosh Kumar},
journal= {arXiv preprint arXiv:2006.02238},
year = {2020}
}
Comments
22 pages, 3 figures. Mathematica files included. To view these files, please download and extract the zipped source file listed under "Other formats"