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

Olivier Marchal (1)

1 PSPM - Probabilités, statistique, physique mathématique

The purpose of the article is to provide partial proofs for two conjectures given by Witte and Forrester in "Moments of the Gaussian β Ensembles and the large N expansion of the densities" with the use of the topological recursion adapted for general β 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

Domaines: Physique mathématique [math-ph]

Olivier Marchal. Elements of proof for conjectures of Witte and Forrester about the combinatorial structure of Gaussian β Ensembles. Journal of High Energy Physics, 2014, 3 (1), pp.1029-8479. ⟨10.1007/JHEP09(2014)003⟩. ⟨hal-01062803⟩