Determinants of Random Unitary Pencils
Functional Analysis
2025-06-06 v1 Mathematical Physics
math.MP
Abstract
We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by integrating against the Haar measure on the unitary group. We obtain an exact formula in the case of scalar coefficients, and conjecture an asymptotic formula in the general case, and prove a special case of the conjecture.
Cite
@article{arxiv.2506.04400,
title = {Determinants of Random Unitary Pencils},
author = {Michael T. Jury and George Roman},
journal= {arXiv preprint arXiv:2506.04400},
year = {2025}
}
Comments
49 pages