Random Kähler metrics

Frank Ferrari; Semyon Klevtsov; Steve Zelditch

doi:10.1016/j.nuclphysb.2012.11.020

Random Kähler metrics

Frank Ferrari^*, Semyon Klevtsov, Steve Zelditch

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a Kähler manifold. The main idea is to use finite dimensional spaces of Bergman metrics, as an approximation to the full space of Kähler 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 Kähler metrics. Several examples are considered.

Original language	English (US)
Pages (from-to)	89-110
Number of pages	22
Journal	Nuclear Physics B
Volume	869
Issue number	1
DOIs	https://doi.org/10.1016/j.nuclphysb.2012.11.020
State	Published - Apr 1 2013

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.nuclphysb.2012.11.020

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abstract = "The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a K{\"a}hler manifold. The main idea is to use finite dimensional spaces of Bergman metrics, as an approximation to the full space of K{\"a}hler 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{\"a}hler metrics. Several examples are considered.",

author = "Frank Ferrari and Semyon Klevtsov and Steve Zelditch",

note = "Funding Information: We would like to thank M. Douglas for useful discussions. This work is supported in part by the Belgian FRFC (grant 2.4655.07 ), the Belgian IISN (grants 4.4511.06 and 4.4514.08 ), the IAP Programme (Belgian Science Policy) , the RFBR grants 11-01-00962 and 12-01-33071 (mol_a_ved), by the Ministry of Education and Science of the Russian Federation under contract 14.740.11.0081 and the NSF grant # DMS-0904252 .",

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Random Kähler metrics

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