Heat kernel estimates for FIN processes associated with resistance forms

TL;DR

This paper establishes heat kernel estimates for FIN processes on resistance form spaces, including fractals, providing new insights even for one-dimensional cases.

Contribution

It introduces novel heat kernel estimates for FIN processes on resistance spaces, extending to fractals like the Sierpinski gasket and carpet.

Findings

Heat kernel estimates are established for FIN processes.

Results apply to fractal spaces such as Sierpinski gasket and carpet.

Findings are new even for one-dimensional FIN diffusion.

Abstract

Quenched and annealed heat kernel estimates are established for Fontes-Isopi-Newman (FIN) processes on spaces equipped with a resistance form. These results are new even in the case of the one-dimensional FIN diffusion, and also apply to fractals such as the Sierpinski gasket and carpet.