Two-dimensional Coulomb gases: Off-diagonal boundary universality
Mathematical Physics Seminar
21st October 2022, 1:45 pm – 3:30 pm
Fry Building, 2.04
The two-dimensional Coulomb gas is (at a specific temperature) a determinantal point process. As the number of points increases, they concentrate on a compact set called the droplet. It is expected that points on the boundary of the droplet have relatively strong correlations. This was shown in the specific case of the elliptic Ginibre ensemble by Forrester and Jancovici in a paper from 1995.
The correlation kernel corresponding to the Coulomb gas is the reproducing kernel of a space of weighted analytic polynomials. Using Hedenmalm and Wennman's techniques for orthogonal polynomials, we study the correlation kernel off-diagonally at the boundary of the droplet. We obtain a limiting kernel related to the reproducing kernel of a Hardy space and show that points on the boundary are indeed strongly correlated. This talk is based on a joint work with Yacin Ameur.
Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/9df8889459d54e5c879ca651cf1651ed1d