Determinants of Random Unitary Pencils

Fuente: arXiv
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Main Authors: Jury, Michael T., Roman, George
Format: Preprint
Published: 2025
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author Jury, Michael T.
Roman, George
author_facet Jury, Michael T.
Roman, George
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_04400
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Determinants of Random Unitary Pencils
Jury, Michael T.
Roman, George
Functional Analysis
Mathematical Physics
15A52, 15A15, 46L54, 46E22
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.
title Determinants of Random Unitary Pencils
topic Functional Analysis
Mathematical Physics
15A52, 15A15, 46L54, 46E22
url https://arxiv.org/abs/2506.04400