Stochastic Kähler geometry: from random zeros to random metrics

Abstract

We provide a survey of results on the statistics of random sections of holomorphic line bundles on Kähler 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' Kähler metrics induced by these random sections.

Survey article, 31 pages