On the moments of the partition function of the CβE field

2020/11/20 by Theodoros Assiotis, Assiotis, Theodoros
Economics, Econometrics and Finance · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2011.10323

openalex publication_date 2020/11/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We obtain a combinatorial formula for the positive integer moments of the partition function of the CβE_N field, or equivalently the moments of the moments of the characteristic polynomial of the CβE_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.

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