Shiping Cao, Hua Qiu
Abstract
We construct a Sierpinski carpet like fractal, on which a diffusion with sub-Gaussian heat kernel estimate does not exist, in contrast to previous researches on the existence of such diffusions, on the generalized Sierpinski carpets and recently introduced unconstrained Sierpinski carpets.
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We construct a Sierpinski carpet like fractal, on which a diffusion with sub-Gaussian heat kernel estimate does not exist, in contrast to previous researches on the existence of such diffusions, on the generalized Sierpinski carpets and recently introduced unconstrained Sierpinski carpets.
Key concepts: Sierpinski triangle, Sierpinski carpet, Fractal, Gaussian, Heat kernel, Mathematics, Diffusion, Statistical physics