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

Jeremiah Anthony Buckley; Mikhail Sodin

doi:10.1007/s10955-017-1813-z

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

Jeremiah Anthony Buckley, Mikhail Sodin

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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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 language	English
Pages (from-to)	300-330
Journal	Journal of Statistical Physics
Volume	168
Issue number	2
Early online date	22 May 2017
DOIs	https://doi.org/10.1007/s10955-017-1813-z
Publication status	Published - Jul 2017

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Fluctuations of the Increment_BUCKLEY_Publishedonline22May2017_GREEN AAMAccepted author manuscript, 508 KBLicence: Unspecified

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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.",

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AB - 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.

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

Abstract

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