CRM: Centro De Giorgi
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From order to chaos - Pisa 2018

A functional limit theorem for the sine-process

speaker: Andrey Dymov (Steklov Mathematical Institute of RAS)

abstract: Determinantal random point processes form an important class of random point processes and naturally arise in different areas of mathematics. In particular, in the random matrix theory, mathematical physics and the number theory. One of the most known determinantal processes in the sine-process. It is well-known that a large class of determinantal processes including the sine-process satisfies the Central Limit Theorem. For many dynamical systems satisfying the CLT the Donsker Invariance Principle also takes place. The latter states that trajectories of the system can be approximated by trajectories of the Brownian motion, in appropriate sense. I will present my joint work with A. Bufetov, where we prove a functional limit theorem for the sine-process, which turns out to be very different from the Donsker Invariance Principle. We show that the anti-derivative of our process can be approximated by the sum of a linear Gaussian process and small independent Gaussian fluctuations which are governed in appropriate sense by the Gaussian Free Field on the plane.

Wed 11 Apr, 10:30 - 11:20, Aula Dini
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