Dipartimento di Scienze Statistiche

7 maggio 2026 ore 14.00 aula 24   Small-time asymptotic behavior of the spectral heat content for isotropic Lévy processes     Prof. Kei Kobayashi (Fordham University - New York)  Abstract: The spectral heat content (SHC) measures the total heat contained in a bounded domain at a given time when the initial temperature inside the domain is set to be one, and the temperature outside the domain is kept at zero. The SHC with heat particles represented by Brownian motion was intensively studied more than three decades ago, whereas the investigation of the SHC for Lévy processes started only about a decade ago. In this talk, we derive the precise small-time asymptotic behavior of the SHC for a large class of isotropic Lévy processes. The result covers the cases of Brownian motion, stable Lévy processes, and some jump diffusions, while the proof provides a unified approach to the asymptotic behavior of the SHC for all of these processes. This is joint work with Hyunchul Park.