Probability Seminar - Hyunchul Park

Institution: State University of New York
Title: Spectral heat content for Levy processes
Date: March 22, 2018
Location: C405 Wells Hall
Time: 3:00 PM - 3:50 PM

Abstract:
In this talk, we study a short time asymptotic behavior of spectral heatcontent for Levy processes. The spectral heat content of a domain D can be interpreted as the amount of heat if the initial temperature on D is 1 and temperature outside D is identically 0 and the motion of heat particle is governed by underlying Levy processes.
We study spectral heat content for arbitrary open sets with finite Lebesgue measure in a real line under some growth condition on the characteristic exponents of the Levy processes. We observe that the behavior is very different from the classical heat content for Brownian motions. We also study the spectral heat content in general dimensions when the processes are of bounded variation. Finally we prove that asymptotic expansion of spectral heat content is stable under integrable perturbation when heat loss is sufficiently large.

This is a joint work with Renming Song and Tomasz Grzywny.