Fluctuations of the Increment of the Argument for the Gaussian Entire Function

Jeremiah Buckley, Mikhail Sodin

Research output: Contribution to journalArticlepeer-review

Abstract

The Gaussian entire function is a random entire function, characterised by a certain invariance with respect to isometries of the plane. We study the fluctuations of the increment of the argument of the Gaussian entire function along planar curves. We introduce an inner product on finite formal linear combinations of curves (with real coefficients), that we call the signed length, which describes the limiting covariance of the increment. We also establish asymptotic normality of fluctuations.

Original languageEnglish
Pages (from-to)300-330
Number of pages31
JournalJournal of Statistical Physics
Volume168
Issue number2
DOIs
StatePublished - 1 Jul 2017

Keywords

  • Gaussian processes
  • Point processes
  • Zeroes of holomorphic functions

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