Probability Seminar: The planar Coulomb gas on a Jordan curve


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April 2, 2024 1:30 pm - 3:00 pm
Science Center 232

Klara Courteaut - Courant Institute, New York University

The eigenvalues of a uniformly distributed unitary matrix 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, at any positive temperature. I will show how to obtain the asymptotic partition function and Laplace transform of a linear statistic. These can be expressed using either the exterior conformal mapping of the curve or its associated Grunsky operator. Based on joint work with Kurt Johansson.