Fluctuations of the increment of the argument for the Gaussian entire function
Complex Variables
2017-08-02 v1 Mathematical Physics
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1608.05590,
title = {Fluctuations of the increment of the argument for the Gaussian entire function},
author = {Jeremiah Buckley and Mikhail Sodin},
journal= {arXiv preprint arXiv:1608.05590},
year = {2017}
}
Comments
33 pages, 7 figures