Elements of proof for conjectures of Witte and Forrester about the combinatorial structure of Gaussian Beta Ensembles

Abstract

The purpose of the article is to provide partial proofs for two conjectures given by Witte and Forrester in "Moments of the Gaussian $\beta$ Ensembles and the large $N$ expansion of the densities" with the use of the topological recursion adapted for general $\beta$ Gaussian case. In particular, the paper uses a version at coinciding points that provides a simple proof for some of the coefficients involved in the conjecture. Additionally, we propose a generalized version of the conjectures for all correlation functions evaluated at coinciding points.

arXiv comment18 pages, version accepted in JHEP, minor mistakes corrected

References in corpus (10)

• Matrix Models for Beta Ensembles
• All genus correlation functions for the hermitian 1-matrix model
• Beta ensembles, stochastic Airy spectrum, and a diffusion
• Asymptotic expansion of beta matrix models in the one-cut regime
• Invariant $\beta$-ensembles and the Gauss-Wigner crossover
• Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
• The uses of the refined matrix model recursion
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• Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry
• Tracy-Widom at high temperature

Cited by in corpus (1)

• Large $N$ expansions for the Laguerre and Jacobi $\beta$ ensembles from the loop equations