Heat kernel lower bound estimates for symmetric pure jump processes via averaged jump kernels

Zhen-Qing Chen; Jun Kigami

Heat kernel lower bound estimates for symmetric pure jump processes via averaged jump kernels

Probability 2026-06-30 v1

Authors: Zhen-Qing Chen , Jun Kigami

Abstract

We derive a heat kernel lower bound estimate for symmetric pure jump processes on general volume doubling metric measure spaces with possible degenerate and/or singular jump kernels using averaged jump kernels. As an application, the main result of this paper is applied to derive a lower bound estimate for the transition density function of the trace of Brownian motions on Sierpinski gaskets on the bottom of the Sierpinski gasket.

Keywords

heat kernel lower bound pure jump processes averaged jump kernels metric measure spaces Sierpinski gasket trace of Brownian motion

Cite

@article{arxiv.2606.31287,
  title  = {Heat kernel lower bound estimates for symmetric pure jump processes via averaged jump kernels},
  author = {Zhen-Qing Chen and Jun Kigami},
  journal= {arXiv preprint arXiv:2606.31287},
  year   = {2026}
}