Ewens measures on compact groups and hypergeometric kernels

Paul Bourgade, Ashkan Nikeghbali, Alain Rouault

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure, these factors become independent random variables with explicit distributions. Beyond the known results on the orthogonal and unitary groups (O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family of probability changes analogous to the biassing in the Ewens sampling formula known for the symmetric group. Then we study the spectral properties of these measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The associated orthogonal polynomials give rise, as n tends to infinity to a limit kernel at the singularity.

Original languageEnglish (US)
Title of host publicationSeminaire de Probabilites XLIII
PublisherSpringer Verlag
Pages351-377
Number of pages27
ISBN (Print)9783642152160
DOIs
StatePublished - 2011

Publication series

NameLecture Notes in Mathematics
Volume2006
ISSN (Print)0075-8434

Keywords

  • Characteristic polynomials
  • Correlation kernel
  • Decomposition of Haar measure
  • Ewens sampling formula
  • Random matrices

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Ewens measures on compact groups and hypergeometric kernels'. Together they form a unique fingerprint.

  • Cite this

    Bourgade, P., Nikeghbali, A., & Rouault, A. (2011). Ewens measures on compact groups and hypergeometric kernels. In Seminaire de Probabilites XLIII (pp. 351-377). (Lecture Notes in Mathematics; Vol. 2006). Springer Verlag. https://doi.org/10.1007/978-3-642-15217-7_15