Asymptotics of non-integer moments of the logarithmic derivative of characteristic polynomials over $SO(2N+1)$

TL;DR

This paper analyzes the asymptotic behavior of non-integer moments of the logarithmic derivative of characteristic polynomials in the $SO(2N+1)$ ensemble, extending previous work on integer moments in related groups.

Contribution

It extends the asymptotic analysis from integer to non-integer moments for the logarithmic derivative of characteristic polynomials in the $SO(2N+1)$ ensemble.

Findings

Derived asymptotics for non-integer moments of the logarithmic derivative.

Extended previous integer moment results to non-integer cases.

Connected results to earlier work on $SO(N)$ and $USp(2N)$ ensembles.

Abstract

This work computes the asymptotics of the non-integer moments of the logarithmic derivative of characteristic polynomials of matrices from the $SO(2N+1)$ ensemble. It follows from work of Alvarez and Snaith who computed the asymptotics of the integer moments of the same statistic over both $SO(N)$ ensembles as well as the $USp(2N)$ ensemble.