Small-time heat decay for stable processes on fractal drums
Probability
2026-03-17 v1
Abstract
In this paper, we study the spectral heat content for isotropic stable processes on fractal drums (namely, open sets with fractal boundaries). The spectral heat content for subordinate killed Brownian motions by stable subordinators was investigated in \cite{PX23}, and the present work serves as a natural extension of \cite{PX23} for the spectral heat content for stable processes. Under suitable geometric conditions on the underlying domains, we show that the decay rate of the spectral heat content for stable processes differs substantially from that for subordinate killed Brownian motions when , where is the interior Minkowski dimension of the boundary of the underlying open set.
Keywords
Cite
@article{arxiv.2603.15323,
title = {Small-time heat decay for stable processes on fractal drums},
author = {Hyunchul Park and Yimin Xiao},
journal= {arXiv preprint arXiv:2603.15323},
year = {2026}
}