Probability and Mathematical Physics Seminar

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The planar Coulomb gas on a Jordan curve

Speaker: Klara Courteaut, Courant Institute

Location: Warren Weaver Hall 1302

Date: Friday, December 15, 2023, 11:10 a.m.

Synopsis:

The eigenvalues of a uniformly distributed unitary matrix (CUE) have the physical interpretation of a system of particles subject to a logarithmic pair interaction, restricted to lie on the unit circle and at inverse temperature 2. In this talk, I will present a more general model in which the unit circle is replaced by a sufficiently regular Jordan curve. In a paper with Johansson, we obtained the asymptotic partition function and the Laplace transform of linear statistics at any positive temperature. These can be expressed using either the exterior conformal mapping of the curve or its associated Grunsky operator.