A sufficient condition for random zero sets of Fock spaces

Xiang Fang, Pham Trong Tien

Research output: Contribution to journalArticlepeer-review

Abstract

Let (rn)n=1∞ be a non-decreasing sequence of radii in (0 , ∞) , and let (θn)n=1∞ be a sequence of independent random arguments uniformly distributed in [0 , 2 π). In this paper, we establish a new sufficient condition on the sequence (rn)n=1∞ under which (rneiθn)n=1∞ is almost surely a zero set for Fock spaces. The condition is in terms of the sum of two characteristics involving the counting function. The sharpness of this condition is discussed and examples are presented to illustrate it.

Original languageEnglish
Pages (from-to)291-304
Number of pages14
JournalArchiv der Mathematik
Volume117
Issue number3
DOIs
StatePublished - Sep 2021

Keywords

  • Fock spaces
  • Random zero sets
  • Zero sets

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