A non-canonical diffusion on the Sierpi\'nski carpet

TL;DR

This paper introduces a novel diffusion process on the Sierpiński carpet that adheres to sub-Gaussian heat kernel estimates using a non-standard measure, expanding understanding of diffusions on fractals.

Contribution

It constructs a new diffusion process on the Sierpiński carpet with unique heat kernel properties and a non-standard self-similar measure, differing from classical models.

Findings

Diffusion satisfies sub-Gaussian heat kernel estimates

Uses a non-standard self-similar measure

Advances fractal diffusion theory

Abstract

We constructed a diffusion process on the Sierpi\'nski carpet that satisfies the sub-Gaussian heat kernel estimate with respect to the Euclidean metric and a non-standard self-similar measure.