Journal of the European Mathematical Society
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Table of Contents | JEMS summary
Volume 12, Issue 3, 2010, pp. 655–701
DOI: 10.4171/JEMS/211
Uniqueness of Brownian motion on Sierpiński carpets
Martin T. Barlow (1), Richard F. Bass (2), Takashi Kumagai (3) and Alexander Teplyaev (4)
(1) Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, BC V6T 1Z2, VANCOUVER, CANADA(2) Department of Mathematics, University of Connecticut, CT 06269-3009, STORRS, UNITED STATES
(3) Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa, Sakyo-ku, 606-8502, KYOTO, JAPAN
(4) Department of Mathematics, University of Connecticut, CT 06269-3009, STORRS, UNITED STATES
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.
Keywords: Sierpiński carpet, fractals, diffusions, Brownian motion, uniqueness, Dirichlet forms