A variational characterisation of the $Sine_\beta$ point process

Vienna Probability Seminar

Date: Tuesday, April 9, 2019 15:30 - 16:30
Speaker: Martin Huesmann (Universität Wien)
Location: Uni Wien, HS 11, 2. OG, OMP 1
Series: Mathematics and CS Seminar
Host: M. Beiglböck, N. Berestycki, L. Erdös, J. Maas
Contact: Uni Wien

Abstract:

The Sine_\beta point process is a stationary point process that appears as the limit of a certain system of interacting particles with a logarithmic repulsion, the so called one-dimensional log-gas. In this talk, we give a characterisation of the Sine_\beta process as the unique minimizer of a free energy functional. Our argument is based on the combination of optimal transport ideas for point processes and approximation techniques for log-gases (screening).