When:
Tuesday, February 11, 2025
4:00 PM - 5:00 PM CT
Where: Lunt Hall, 2033 Sheridan Road, Evanston, IL 60208 map it
Audience: Faculty/Staff - Student - Public - Post Docs/Docs - Graduate Students
Contact:
Elton Hsu
(847) 491-8541
Group: Department of Mathematics: Probability Seminar
Category: Lectures & Meetings, Academic
Title: Log-derivatives of the heat kernel and Brownian bridges
Abstract: We first note that derivatives of the heat kernel, for small time, can be effectively localized. This allows us to extend well-known bounds on the logarithmic derivatives of the heat kernel from compact Riemannian manifolds to appropriate compact subsets of incomplete Riemannian, or even sub-Riemannian, manifolds. Moreover, for any pair of points in such a compact, we see that the asymptotics of the log-derivatives of the heat kernel are given by cumulants of geometrically natural random variables with respect to the law of large numbers measure of the corresponding Brownian bridge. This talk is based on joint work with Ludovic Sacchelli.