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Uniqueness of Brownian motion on Sierpiński carpets. (English) Zbl 1200.60070

The authors prove that, 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 Brownian motion is uniquely determined and the Laplacian is well defined.

MSC:

60J65 Brownian motion
60G18 Self-similar stochastic processes
60J35 Transition functions, generators and resolvents
60J60 Diffusion processes
28A80 Fractals
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References:

[1] Alexander, S., Orbach, R.: Density of states on fractals: “fractons”. J. Physique (Paris) Lett. 43, 625-631 (1982)
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