Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials

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.

arXiv commentv3: 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''

References in corpus (5)

• On the averages of characteristic polynomials from classical groups
• Random matrix theory and symmetric spaces
• Properties of some families of hypergeometric orthogonal polynomials in several variables
• Inversion of the Pieri formula for Macdonald polynomials
• Singularity dominated strong fluctuations for some random matrix averages

Cited by in corpus (8)

• Duality in random matrix ensembles for all Beta
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• Matrix models for classical groups and Toeplitz$\pm$Hankel minors with applications to Chern-Simons theory and fermionic models
• Asymptotics for products of characteristic polynomials in classical $\beta$-Ensembles
• Averages of ratios of characteristic polynomials in circular beta-ensembles and super-Jack polynomials
• Maxima of log-correlated fields: some recent developments
• Limits for circular Jacobi beta-ensembles
• Hyperdeterminantal expressions for Jack functions of rectangular shapes