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On the moments of the partition function of the C$β$E field (2011.10323v3)
Published 20 Nov 2020 in math.PR, math-ph, math.CO, and math.MP
Abstract: We obtain a combinatorial formula for the positive integer moments of the partition function of the $C\beta E_{N}$ field, or equivalently the moments of the moments of the characteristic polynomial of the $C\beta E_{N}$ ensemble. We then use this formula to establish the large $N$ asymptotics of these moments in the "moment-supercritical" regime. A key role is played by Jack polynomials.