On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices

被引：2

作者：

Assiotis, Theodoros ^{[1
]}

Bailey, Emma C. ^{[2
]}

Keating, Jonathan P. ^{[3
]}

机构：

[1] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Midlothian, Scotland

[2] CUNY, Grad Ctr, Dept Math, 365 5th Ave, New York, NY 10016 USA

[3] Univ Oxford, Math Inst, Oxford OX2 6GG, England

来源：

ANNALES DE L INSTITUT HENRI POINCARE D | 2022年 / 9卷 / 03期

基金：

欧洲研究理事会;

关键词：

Random matrices; characteristic polynomials; classical groups; moments; Gelfand-Tsetlin patterns; MAXIMUM;

D O I：

10.4171/AIHPD/127

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the matrix-size tends to infinity in terms of the volumes of certain regions involving continuous Gelfand-Tsetlin patterns with constraints. The results we find differ from those in the unitary case considered previously.

引用

页码：567 / 604

页数：38

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