Moments of the logarithmic derivative of characteristic polynomials from $SO(N)$ and $USp(2N)$

Abstract

We study moments of the logarithmic derivative of characteristic polynomials of orthogonal and symplectic random matrices. In particular, we compute the asymptotics for large matrix size, $N$, of these moments evaluated at points which are approaching 1. This follows work of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith where they compute these asymptotics in the case of unitary random matrices.

43 pages. This version has an added discussion and computation of lower order terms. It also contains implemented comments and suggestions from the referee for JMP. Accepted for publication in the Journal of Mathematical Physics

References in corpus (2)

• Mixed moments of characteristic polynomials of random unitary matrices
• A Combinatorial Approach to Mixed Ratios of Characteristic Polynomials

Cited by in corpus (2)

• Joint moments of a characteristic polynomial and its derivative for the circular $\beta$-ensemble
• On the logarithmic derivative of characteristic polynomials for random unitary matrices