Abstract: In this talk, I will describe a construction of random meromorphic functions with prescribed simple poles with unit residues at a given stationary point process in the plane. These 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.
I plan to describe for which point processes these electric fields, after subtracting the mean, become stationary, and discuss how they may be used to study the growth of the number variance (“charge fluctuations”) of stationary point processes in dilations of Jordan domains with quite irregular boundaries.
This talk is based on recent joint work with Misha Sodin and Oren Yakir (Tel Aviv) (see https://arxiv.org/abs/2211.01312 and https://arxiv.org/abs/2210.09882)
