Stochastic K\"ahler geometry: from random zeros to random metrics
Complex Variables
2023-03-22 v1 Algebraic Geometry
Differential Geometry
Probability
Abstract
We provide a survey of results on the statistics of random sections of holomorphic line bundles on K\"ahler manifolds, with an emphasis on the resulting asymptotics when a line bundle is raised to increasing tensor powers. We conclude with a brief discussion of the `Bergman' K\"ahler metrics induced by these random sections.
Cite
@article{arxiv.2303.11559,
title = {Stochastic K\"ahler geometry: from random zeros to random metrics},
author = {Bernard Shiffman and Steve Zelditch},
journal= {arXiv preprint arXiv:2303.11559},
year = {2023}
}
Comments
Survey article, 31 pages