A Generalization of Random Matrix Ensemble II: Concrete Examples and Integration Formulae

TL;DR

This paper provides concrete examples of generalized random matrix ensembles, deriving their joint density functions and integration formulas, including classical and new ensembles, unifying various cases under a single framework.

Contribution

It introduces a unified approach to derive joint density functions and integration formulas for a broad class of generalized random matrix ensembles.

Findings

Derived joint density functions for multiple ensembles

Unified framework simplifies classical and new ensemble analysis

Provided classical and variation forms of integration formulas

Abstract

According to the classification scheme of the generalized random matrix ensembles, we present various kinds of concrete examples of the generalized ensemble, and derive their joint density functions in an unified way by one simple formula which was proved in [2]. Particular cases of these examples include Gaussian ensemble, chiral ensemble, new transfer matrix ensembles, circular ensemble, Jacobi ensembles, and so on. The associated integration formulae are also given, which are just many classical integration formulae or their variation forms.