A non-canonical diffusion on the Sierpiński carpet

2025/11/27 by Shiping Cao, Cao, Shiping, Hua Qiu +2
Mathematics · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2511.22156

Abstract

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

Citations

• Conductive homogeneity of locally symmetric polygon-based self-similar sets
• Heat kernel for reflected diffusion and extension property on uniform domains
• Self-similar Dirichlet forms on polygon carpets
• Conductive homogeneity of compact metric spaces and construction of p-energy
• Dirichlet forms on unconstrained Sierpinski carpets
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets

Related

• Metrics on the Sierpinski carpet by weight functions
• A Sierpinski carpet like fractal without standard self-similar energy
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Heat kernel for reflected diffusion and extension property on uniform domains
• Sub-Gaussian heat kernel estimates for reflected diffusion on inner uniform domains