Uniqueness of Brownian motion on Sierpinski carpets
نویسندگان
چکیده
We 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. Research partially supported by NSERC (Canada), and EPSRC (UK). Research partially supported by NSF grant DMS-0601783. Corresponding author Research partially supported by the Grant-in-Aid for Scientific Research (B) 18340027. Research partially supported by NSF grant DMS-0505622.
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