Header

UZH-Logo

Maintenance Infos

The characteristic polynomial on compact groups with Haar measure: some equalities in law


Bourgade, P; Nikeghbali, A; Rouault, A (2007). The characteristic polynomial on compact groups with Haar measure: some equalities in law. Comptes Rendus Mathematique, 345(4):229-232.

Abstract

This Note presents some equalities in law for ZN:=det(Id−G), where G is an element of a subgroup of the set of unitary matrices of size N, endowed with its unique probability Haar measure. Indeed, under some general conditions, ZN can be decomposed as a product of independent random variables, whose laws are explicitly known. Our results can be obtained in two ways: either by a recursive decomposition of the Haar measure (Section 1) or by previous results by Killip and Nenciu (2004) on orthogonal polynomials with respect to some measure on the unit circle (Section 2). This latter method leads naturally to a study of determinants of a class of principal submatrices (Section 3).

Abstract

This Note presents some equalities in law for ZN:=det(Id−G), where G is an element of a subgroup of the set of unitary matrices of size N, endowed with its unique probability Haar measure. Indeed, under some general conditions, ZN can be decomposed as a product of independent random variables, whose laws are explicitly known. Our results can be obtained in two ways: either by a recursive decomposition of the Haar measure (Section 1) or by previous results by Killip and Nenciu (2004) on orthogonal polynomials with respect to some measure on the unit circle (Section 2). This latter method leads naturally to a study of determinants of a class of principal submatrices (Section 3).

Statistics

Citations

1 citation in Web of Science®
1 citation in Scopus®
Google Scholar™

Altmetrics

Downloads

47 downloads since deposited on 07 Dec 2009
6 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2007
Deposited On:07 Dec 2009 10:42
Last Modified:06 Dec 2017 20:41
Publisher:Elsevier
ISSN:1631-073X
Publisher DOI:https://doi.org/10.1016/j.crma.2007.06.023
Related URLs:http://arxiv.org/abs/0706.3057

Download

Download PDF  'The characteristic polynomial on compact groups with Haar measure: some equalities in law'.
Preview
Content: Accepted Version
Filetype: PDF
Size: 1MB
View at publisher