A generalization of random matrix ensemble, I: General theory

Jinpeng An, Zhengdong Wang and Kuihua Yan

Vol. 228 (2006), No. 1, 1–17

DOI: 10.2140/pjm.2006.228.1

Abstract

We give a generalization of random matrix ensembles, which includes all classical ensembles. We derive the joint-density function of the generalized ensemble by one simple formula, giving a direct and unified way to compute the density functions for all classical ensembles and various kinds of new ensembles. An integration formula associated with the generalized ensembles is given. We propose a taxonomy of generalized ensembles encompassing all classical ensembles and some new ones not considered before.

Keywords

random matrix ensemble, Lie group, integration formula

Mathematical Subject Classification 2000

Primary: 15A52

Secondary: 58C35, 57S25

Milestones

Received: 8 February 2005

Accepted: 13 April 2005

Published: 1 November 2006