On the moments of the partition function of the C$\beta$E field
Probability
2022-03-14 v3 Mathematical Physics
Combinatorics
math.MP
Abstract
We obtain a combinatorial formula for the positive integer moments of the partition function of the field, or equivalently the moments of the moments of the characteristic polynomial of the ensemble. We then use this formula to establish the large asymptotics of these moments in the "moment-supercritical" regime. A key role is played by Jack polynomials.
Keywords
Cite
@article{arxiv.2011.10323,
title = {On the moments of the partition function of the C$\beta$E field},
author = {Theodoros Assiotis},
journal= {arXiv preprint arXiv:2011.10323},
year = {2022}
}
Comments
Improvements following referee reports. To appear Journal of Statistical Physics