A sufficient condition for random zero sets of Fock spaces

Xiang Fang, Pham Trong Tien

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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
Issue number3
StatePublished - Sep 2021


  • Fock spaces
  • Random zero sets
  • Zero sets


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