The random Weierstrass zeta function I. Existence, uniqueness, fluctuations
Probability
2023-10-24 v2 Mathematical Physics
Complex Variables
math.MP
Abstract
We describe a construction of random meromorphic functions with prescribed simple poles with unit residues at a given stationary point process. We characterize those stationary processes with finite second moment for which, after subtracting the mean, the random function becomes stationary. These random meromorphic functions can be viewed as random analogues of the Weierstrass zeta function from the theory of elliptic functions, or equivalently as electric fields generated by an infinite random distribution of point charges.
Cite
@article{arxiv.2210.09882,
title = {The random Weierstrass zeta function I. Existence, uniqueness, fluctuations},
author = {Mikhail Sodin and Aron Wennman and Oren Yakir},
journal= {arXiv preprint arXiv:2210.09882},
year = {2023}
}
Comments
41 pages