Year: 2024
Type: preprint
Abstract: Hypergeometric functions of complex matrices were introduced by James in multivariate statistics. These special functions play many roles in random matrix theory. The main goal of this paper is to suggest a new use for them as holomorphic observables of the Circular Unitary Ensemble. We analyze the high-dimensional behavior of the expected derivatives of these random analytic functions, and show that they admit asymptotic expansions which can be described in terms of quasimodular forms, giving an apparently new connection between the CUE and number theory.
Source: arXiv (Cornell University)
Author: Novak, Jonathan
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403322590