seminar: The Allen-Cahn action functional and its sharp interface limit
speaker: Matthias Roeger (Max Planck Institute for Mathematics in the Sciences Leipzig)abstract: Stochastic perturbations of phase field equations allow for events that are out of the scope of deterministic models, as for example the switching between two stable states. Large deviation theory estimates the probability of such events in terms of a (deterministic) action functional. Extending previous work by Kohn, Otto, Reznikoff and Vanden-Eijnden we consider the Allen-Cahn action functional in a particular scaling that exhibits a competition between nucleation and propagation costs. Our focus is on a lower bound that is sharp even in the case that higher multiplicities of the limiting phase interfaces occur. Our approach is based on techniques from Geometric Measure Theory and uses a generalized formulation of evolving hypersurfaces similar to that of Brakke for the mean curvature flow.
timetable:
Wed 28 May, 16:30 - 17:30, Aula Dini
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