Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials

Details Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials

2006-08-30

arxiv.org/abs/math/0608751v3

J. Phys. A: Math. Theor. 40 (2007) 13567-13586

Mathematics

Probability

v3: 18 pages, major revision containing additional results; the title of v1 is ``Two parameters circular ensembles and Jacobi-

Scientific paper

10.1088/1751-8113/40/45/006

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.

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