Complex determinantal processes and H1 noise
Probability
2021-03-23 v1 Mathematical Physics
math.MP
Abstract
For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinantal point processes with intensity rho dnu, where nu is the corresponding invariant measure. We show that as rho converges to infinity, after centering, these processes converge to invariant H1 noise. More precisely, for all functions f in the interesection of H1(nu) and L1(nu) the distribution of sum f(z) - rho/pi integral f dnu converges to Gaussian with mean 0 and variance given by ||f||_H1^2 / (4 pi).
Cite
@article{arxiv.math/0608785,
title = {Complex determinantal processes and H1 noise},
author = {Brian Rider and Balint Virag},
journal= {arXiv preprint arXiv:math/0608785},
year = {2021}
}
Comments
22 pages, 1 figure