Correlation Functions for \beta=1 Ensembles of Matrices of Odd Size

TL;DR

This paper rederives correlation functions for eta=1 ensembles of N x N matrices with odd size using Tracy and Widom's method, focusing on Hermitian and real asymmetric cases.

Contribution

It provides a new derivation of correlation functions specifically for odd-sized eta=1 matrix ensembles, extending previous results.

Findings

Correlation functions for eta=1 ensembles of odd-sized matrices are explicitly derived.

The method of Tracy and Widom is effectively applied to these ensembles.

Results enhance understanding of spectral properties of eta=1 matrices with odd dimensions.

Abstract

Using the method of Tracy and Widom we rederive the correlation functions for \beta=1 Hermitian and real asymmetric ensembles of N x N matrices with N odd.