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

References in corpus (8)

• 2D Gravity and Random Matrices
• Bergman Kernel from Path Integral
• Lectures on Stability and Constant Scalar Curvature
• Gravitational Actions in Two Dimensions and the Mabuchi Functional
• Random Kähler Metrics
• Random Geometry, Quantum Gravity and the Kähler Potential
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Cited by in corpus (7)

• Heavy Tails in Calabi-Yau Moduli Spaces
• Random normal matrices, Bergman kernel and projective embeddings
• Random Kähler Metrics
• Multi-Loop Zeta Function Regularization and Spectral Cutoff in Curved Spacetime
• Stability and integration over Bergman metrics
• Disordered statistical physics in low dimensions: extremes, glass transition, and localization
• Asymptotic expansion of the off-diagonal Bergman kernel on compact Kähler manifolds