Two-parameter circular ensembles and Macdonald polynomials
نویسنده
چکیده
We define a new probability measure with two parameters on the n-dimensional torus. A q-analogue of Dyson’s circular ensembles is seen to be a special case of the new measure. The moments of the characteristic polynomial with respect to the measure are calculated via Macdonald function theory. Furthermore, explicit expressions for the asymptotic behavior of the moments in the limit as n → ∞ are obtained. MSC-class: primary 15A52; secondary 05E05.
منابع مشابه
Two parameters circular ensembles and Jacobi-Trudi type formulas for Jack functions of rectangular shapes
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تاریخ انتشار 2006