Averages of ratios of characteristic polynomials in circular β-ensembles and super-Jack polynomials
نویسنده
چکیده
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 dualities for ratio averages between β and 4/β. MSC-class: primary 15A52; secondary 05E05, 15A15
منابع مشابه
Products and Ratios of Characteristic Polynomials of Random Hermitian Matrices
denotes the average of f with respect to dPa ,N . Recently there has been considerable interest in the averages of products and ratios of the characteristic polynomials DN@m ,H#5P i51 N (m2xi(H)) of random matrices with respect to various ensembles. Such averages are used, in particular, in making predictions about the moments of the Riemann-zeta function @see Refs. 12–14 ~circular ensembles! a...
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