Ensemble Averages when \beta is a Square Integer

TL;DR

This paper introduces a hyperpfaffian approach to compute partition functions and ensemble averages for specific Hermitian and circular ensembles characterized by particular integer values of 2, expanding the mathematical tools available for these random matrix models.

Contribution

It provides a novel hyperpfaffian formulation for ensemble averages in Hermitian and circular ensembles at special 2 values, generalizing previous methods.

Findings

Hyperpfaffian formulas for 2=L^2 and 2=L^2+1 cases.

Unified approach for Hermitian and circular ensembles.

Enhanced computational techniques for ensemble averages.

Abstract

We give a hyperpfaffian formulation of partition functions and ensemble averages for Hermitian and circular ensembles when L is an arbitrary integer and \beta=L^2 and when L is an odd integer and \beta=L^2 +1.