Simple matrix models for random Bergman metrics

TL;DR

This paper explores simple matrix models for random Bergman metrics, linking probability measures on Kahler manifolds to matrix models, and computes correlation functions, especially focusing on the Wishart model.

Contribution

It introduces explicit matrix models for random metrics on Kahler manifolds and computes their correlation functions, including detailed analysis of the Wishart model.

Findings

Computed one and two-point functions of the metric.

Established connections between geometric correlation functions and matrix model correlators.

Provided detailed analysis of the Wishart matrix model.

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.