Probability and Mathematical Physics Seminar

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The Bargmann-Fock excess for the randomly perturbed lattice

Speaker: Mikhail Sodin, Tel Aviv University

Location: Warren Weaver Hall 1302

Date: Friday, November 6, 2026, noon

Synopsis:

A classical theorem of Perelomov states that the standard square lattice,with one point removed, is a uniqueness set for the Bargmann-Fock space of entire functions, while removing two points produces the zero set of a nonzero Bargmann-Fock function. In ongoing work with Alexander Borichev, we consider the same question for the random point process obtained by perturbing the square lattice by independent complex Gaussian variables. The answer depends on the size of the perturbation and — somewhat unexpectedly —  on the tools from the theory of log-correlated fields.

If time permits, I will also discuss the answer to a similar question concerning the excess of the sine-beta point process in the Paley-Wiener space of entire function, obtained in a work in progress in with Paul Bourgade and Ofer Zeitouni.