On the moments of the partition function of the C$\beta$E field

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.

arXiv commentImprovements following referee reports. To appear Journal of Statistical Physics