MIT Probability Seminar
Monday, March 01, 2021 at 4:15pm to 5:15pm
Virtual EventFeatured Speaker : Tom Alberts (University of Utah)
Title : Loewner Dynamics for the Multiple SLE(0) Process
Abstract : Recently Peltola and Wang introduced the multiple SLE(0) process as the deterministic limit of the random multiple SLE(κ) curves as κ goes to zero. They prove this result by means of a ``small κ" large deviations principle, but the limiting curves also turn out to have important geometric characterizations that are independent of their relation to SLE(κ). In particular, they show that the SLE(0) curves can be generated by a deterministic Loewner evolution driven by multiple points, and the vector field describing the evolution of these points must satisfy a particular system of algebraic equations. We show how to generate solutions to these algebraic equations in two ways: first in terms of the poles and critical points of an associated real rational function, and second via the well-known Calogero-Moser integrable system with particular initial velocities. Although our results are purely deterministic they are again motivated by taking limits of probabilistic constructions, which I will explain.
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