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
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas
Contact
Url
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).