Barlow, Martin T.; Bass, Richard F.; Kumagai, Takashi; Teplyaev, Alexander Uniqueness of Brownian motion on Sierpiński carpets. (English) Zbl 1200.60070 J. Eur. Math. Soc. (JEMS) 12, No. 3, 655-701 (2010). 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. Reviewer: D. R. Bell (Jacksonville) Cited in 57 Documents MSC: 60J65 Brownian motion 60G18 Self-similar stochastic processes 60J35 Transition functions, generators and resolvents 60J60 Diffusion processes 28A80 Fractals Keywords:Sierpinski carpet; fractals; diffusions, Brownian motion; uniqueness; Dirichlet forms PDFBibTeX XMLCite \textit{M. T. Barlow} et al., J. Eur. Math. Soc. (JEMS) 12, No. 3, 655--701 (2010; Zbl 1200.60070) Full Text: DOI arXiv Link References: [1] Alexander, S., Orbach, R.: Density of states on fractals: “fractons”. J. Physique (Paris) Lett. 43, 625-631 (1982) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.