Geodesic
Uniqueness of Brownian motion on Sierpiński carpets
Journal of the European Mathematical Society, Tome 12 (2010) no. 3, pp. 655-701.

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/211
Classification : 60-XX, 37-XX, 00-XX
Keywords: Sierpiński carpet, fractals, diffusions, Brownian motion, uniqueness, Dirichlet forms 
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Martin T. Barlow; Richard F. Bass; Takashi Kumagai; Alexander Teplyaev. Uniqueness of Brownian motion on Sierpiński carpets. Journal of the European Mathematical Society, Tome 12 (2010) no. 3, pp. 655-701. doi : 10.4171/jems/211. http://geodesic.mathdoc.fr/articles/10.4171/jems/211/

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