Uniqueness of Brownian motion on Sierpiński carpets
Martin T. Barlow
The University of British Columbia, Vancouver, CanadaRichard F. Bass
University of Connecticut, Storrs, United StatesTakashi Kumagai
Kyoto University, JapanAlexander Teplyaev
University of Connecticut, Storrs, USA
Abstract
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.
Cite this article
Martin T. Barlow, Richard F. Bass, Takashi Kumagai, Alexander Teplyaev, Uniqueness of Brownian motion on Sierpiński carpets. J. Eur. Math. Soc. 12 (2010), no. 3, pp. 655–701
DOI 10.4171/JEMS/211