Eigenphase distributions of unimodular circular ensembles
Mathematical Physics
2024-02-06 v2 Disordered Systems and Neural Networks
High Energy Physics - Lattice
High Energy Physics - Theory
math.MP
Abstract
Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices (=2), supported by explicit examples at small N and by numerical samplings at larger N. In this note, I spell out a concise proof of their formula, and present its orthogonal and symplectic counterparts, i.e. the eigenphase distributions of Haar-random unimodular symmetric (=1) and selfdual (=4) unitary matrices parametrizing SU(N)/SO(N) and SU(2N)/Sp(2N), respectively.
Keywords
Cite
@article{arxiv.2401.09045,
title = {Eigenphase distributions of unimodular circular ensembles},
author = {Shinsuke Nishigaki},
journal= {arXiv preprint arXiv:2401.09045},
year = {2024}
}
Comments
3 pages, version to appear in PTEP. Contains a friendly comment on a preprint 2310.07533 [hep-th]