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Uniqueness of Laplacian and Brownian motion on Sierpinski carpets

Teplyaev, A (Connecticut)
Tuesday 27 July 2010, 14:00-14.45

Seminar Room 1, Newton Institute


Up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpinski carpet that is invariant with respect to the local symmetries of the carpet. Consequently for each such fractal the law of the Brownian motion is uniquely determined and the Laplacian is well defined. As a consequence, there are uniquely defined spectral and walk dimensions which determine the behavior of the natural diffusion processes by so called Einstein relation (these dimensions are not directly related to the well known Hausdorff dimension, which describes the distribution of the mass in a fractal).


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