English

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.

Keywords

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

R2 v1 2026-06-28T09:25:27.691Z