Large deviations of empirical measures of zeros on riemann surfaces

Steve Zelditch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We determine a large deviations principle (LDP) for the empirical measure of zeros of random holomorphic sections s of random line bundles L→X over a Riemann surface X of genus g≥1. Zeitouni and Zelditch [27] proved such an LDP in the g=0 case of ℂℙ1 using an explicit formula for the joint probability current (JPC) of zeros of Gaussian random polynomials. The main purpose of this article is to define Gaussian-type measures on the "vortex moduli space" of all holomorphic sections of all line bundles of degree N and to calculate its JPC as a volume form on the configuration space X(N) of N points of X.

Original languageEnglish (US)
Pages (from-to)592-664
Number of pages73
JournalInternational Mathematics Research Notices
Issue number3
StatePublished - 2013

ASJC Scopus subject areas

  • Mathematics(all)


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