Feb 10 2025

Analysis and Applied Mathematics Seminar: Log-derivatives of the heat kernel and Brownian bridges, by Robert Neel

February 10, 2025

4:00 PM - 4:50 PM

Location

636 SEO

Address

Chicago, IL

Robert Neel (Lehigh University): Log-derivatives of the heat kernel and Brownian bridges

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.

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Contact

Cheng Ouyang

Date posted

Feb 10, 2025

Date updated

Feb 10, 2025

Speakers