Median and mean of the supremum of L2 normalized random holomorphic fields

Renjie Feng*, Steve Zelditch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We prove that the expected value and median of the supremum of L2 normalized random holomorphic fields of degree n on m-dimensional Kähler manifolds are asymptotically of order mlogn. There is an exponential concentration of measure of the sup norm around this median value. Prior results only gave the upper bound. The estimates are based on the entropy methods of Dudley and Sudakov combined with a precise analysis of the relevant distance functions and covering numbers using off-diagonal asymptotics of Bergman-Szegö kernels. Recent work on the critical value distribution is also used.

Original languageEnglish (US)
Pages (from-to)5085-5107
Number of pages23
JournalJournal of Functional Analysis
Issue number8
StatePublished - Apr 15 2014


  • Random holomorphic sections
  • Supremum

ASJC Scopus subject areas

  • Analysis

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