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Autocorrelations of characteristic polynomials for the Alternative Circular Unitary Ensemble

Published 31 Dec 2022 in math-ph, math.MP, and math.NT | (2301.00268v2)

Abstract: We find closed formulas for arbitrarily high mixed moments of characteristic polynomials of the Alternative Circular Unitary Ensemble (ACUE), as well as closed formulas for the averages of ratios of characteristic polynomials in this ensemble. A comparison is made to analogous results for the Circular Unitary Ensemble (CUE). Both moments and ratios are studied via symmetric function theory and a general formula of Borodin-Olshanski-Strahov.

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