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

Abstract

We study the averages of ratios of characteristic polynomials over circular $\beta$-ensembles, where $\beta$ 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 $\beta$ and $4/\beta$.

This paper has been withdrawn by the author due to a crucial error

References in corpus (3)

• Duality in random matrix ensembles for all Beta
• Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials
• Haar expectations of ratios of random characteristic polynomials

Cited by in corpus (1)

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