Surveys in Differential Geometry

Volume 26 (2021)

Stochastic Kähler geometry: from random zeros to random metrics

Pages: 299 – 334

DOI: https://dx.doi.org/10.4310/SDG.2021.v26.n1.a9

Authors

Bernard Shiffman (Department of Mathematics, Johns Hopkins University, Baltimore, Maryland, U.S.A.)

Steve Zelditch (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)

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.

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Research of the second author was partially supported by NSF grant DMS-1810747.

Published 22 January 2024