Random K\"ahler Metrics
High Energy Physics - Theory
2013-01-15 v2 Mathematical Physics
math.MP
Abstract
The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a K\"ahler manifold. The main idea is to use finite dimensional spaces of Bergman metrics, as an approximation to the full space of K\"ahler metrics. We use the theory of large deviations to decide when a sequence of probability measures on the spaces of Bergman metrics tends to a limit measure on the space of all K\"ahler metrics. Several examples are considered.
Cite
@article{arxiv.1107.4575,
title = {Random K\"ahler Metrics},
author = {Frank Ferrari and Semyon Klevtsov and Steve Zelditch},
journal= {arXiv preprint arXiv:1107.4575},
year = {2013}
}
Comments
22 pages