Student Probability Seminar

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LDP for Interacting Diffusions

Speaker: Elias Hess-Childs, CIMS

Location: Warren Weaver Hall 517

Date: Monday, October 4, 2021, 11:30 a.m.

Synopsis:

After a brief review of large deviation principles and the Friedlin-Wentzell theorem, we will prove that the process level empirical measures of N weakly interacting particles with noise satisfy a LDP, and characterize the rate function. This will use the combination of many important theorems in LDP theory, such as the Contraction Principle, Schilder’s Theorem, Sanov’s Theorem, and Varadhan’s Lemma. We will finish by describing a new result wherein the magnitude of the noise vanishes as the number of interacting particles increases. (Some familiarity with LDPs will be helpful)