The Jancovici - Lebowitz - Manificat law for large fluctuations of random complex zeroes
Probability
2016-12-21 v2 Mathematical Physics
Complex Variables
math.MP
Abstract
By random complex zeroes we mean the zero set of a random entire function whose Taylor coefficients are independent complex-valued Gaussian variables, and the variance of the k-th coefficient is 1/k!. This zero set is distribution invariant with respect to isometries of the complex plane. We study large fluctuations of random complex zeroes and show that they obey the asymptotic law that was discovered some time ago by Jancovici, Lebowitz and Manificat for charge fluctuations of a Coulomb system of particles.
Keywords
Cite
@article{arxiv.0707.3863,
title = {The Jancovici - Lebowitz - Manificat law for large fluctuations of random complex zeroes},
author = {F. Nazarov and M. Sodin and A. Volberg},
journal= {arXiv preprint arXiv:0707.3863},
year = {2016}
}
Comments
34 pages, 1 figure