Averages of ratios of characteristic polynomials in circular beta-ensembles and super-Jack polynomials

2008/05/23 by Sho Matsumoto, Matsumoto, Sho · 1 citation
Mathematics · #05E05 #15A15 (Secondary) #15A52 (Primary) #Advanced Combinatorial Mathematics #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #math.CO #math.PR #msc:05E05 #msc:15A15 #msc:15A52

paper · pdf · doi:10.48550/arxiv.0805.3573

This paper has been withdrawn by the author due to a crucial error

openalex publication_date 2008/05/23 · arxiv created 2014/03/07 · arxiv updated 2014/03/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the averages of ratios of characteristic polynomials over circular β-ensembles, where β is a positive real number. Using Jack polynomial theory, we obtain three expressions for ratio averages. Two of them are given as sums of super-Jack polynomials and another one is given by a hyperdeterminant. As applications, we give dual relations for ratio averages between β and 4/β.

Cited by

• Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators

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