Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials
Probability
2009-11-11 v3 Combinatorics
Abstract
We express the averages of products of characteristic polynomials for random matrix ensembles associated with compact symmetric spaces in terms of Jack polynomials or Heckman and Opdam's Jacobi polynomials depending on the root system of the space. We also give explicit expressions for the asymptotic behavior of these averages in the limit as the matrix size goes to infinity.
Keywords
Cite
@article{arxiv.math/0608751,
title = {Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials},
author = {Sho Matsumoto},
journal= {arXiv preprint arXiv:math/0608751},
year = {2009}
}
Comments
v3: 18 pages, major revision containing additional results; the title of v1 is ``Two parameters circular ensembles and Jacobi-Trudi type formulas for Jack functions of rectangular shapes'' while the title of v2 is ``Two-parameter circular ensembles and Macdonald polynomials''