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

Sho Matsumoto

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arXiv · 0805.3573

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

Sho Matsumoto

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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 $4/\beta$.

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Sho Matsumoto. 2008-05-23. Averages of ratios of characteristic polynomials in circular beta-ensembles and super-Jack polynomials. https://arxiv.org/abs/0805.3573

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