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Explore the asymptotic behavior of planar Coulomb gas systems confined to analytic Jordan arcs in this 45-minute mathematical lecture. Delve into the partition function asymptotics expressed through Fredholm determinants of the newly introduced arc-Grunsky operator and appropriate conformal maps. Compare and contrast this framework with Coulomb gas systems on Jordan curves and their relationship to Loewner energy. Examine the mathematical arguments and proof techniques underlying these results, presented as part of collaborative research with Klara Courteaut and Fredrik Viklund. Gain insights into the intersection of probability theory, complex analysis, and geometric function theory through this advanced mathematical presentation delivered at IPAM's New Interactions Between Probability and Geometry Workshop.
