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

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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
JournalJournal of Statistical Physics
Volume168
Issue number2
Early online date22 May 2017
DOIs
Publication statusPublished - Jul 2017

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