Simple matrix models for random Bergman metrics

Abstract

Recently, the authors have proposed a new approach to the theory of random metrics, making an explicit link between probability measures on the space of metrics on a Kahler manifold and random matrix models. We consider simple examples of such models and compute the one and two-point functions of the metric. These geometric correlation functions correspond to new interesting types of matrix model correlators. We study a large class of examples and provide in particular a detailed study of the Wishart model.

23 pages, IOP Latex style, diastatic function Eq. (22) and contact terms in Eqs. (76, 95) corrected, typos fixed. Accepted to JSTAT