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
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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Date posted
Feb 10, 2025
Date updated
Feb 10, 2025
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