Probability and Mathematical Physics Seminar

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Random Weierstrass zeta-function

Speaker: Mikhail Sodin, Tel Aviv University

Location: Warren Weaver Hall 1302

Date: Friday, October 20, 2023, noon

Synopsis:

Why some stationary planar point processes generate stationary fields with divergence equaled the counting measure of the point process minus the Lebesgue measure (the infinite Ginibre determinantal process and the zero set of the Gaussian Entire Function belong to this class), while others (like the Poisson point process) don't? In the talk we give a simple answer to this question and discuss curious properties of that stationary field, for instance, the logarithmic divergence of their covariance, and the fluctuations of their line integrals. 

A central role will be played by random meromorphic functions having simple poles with unit residues at a given stationary point process. These random meromorphic functions can be viewed as random analogues of the Weierstrass zeta function from the theory of elliptic functions.

If time permits, we will also touch existence of somewhat counter-intuitive  exotic objects generated by stationary planar point processes.

The talk will be based on the joint work with Oren Yakir and Aron Wennman: 

https://arxiv.org/abs/2210.09882 , https://arxiv.org/abs/2211.01312