Uniqueness of Brownian motion on Sierpi&#324ski carpets

  • Richard F. Bass

    University of Connecticut, Storrs, United States
  • Takashi Kumagai

    Kyoto University, Japan
  • Martin T. Barlow

    The University of British Columbia, Vancouver, Canada
  • Alexander Teplyaev

    University of Connecticut, Storrs, USA


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

Richard F. Bass, Takashi Kumagai, Martin T. Barlow, Alexander Teplyaev, Uniqueness of Brownian motion on Sierpi&#324ski carpets. J. Eur. Math. Soc. 12 (2010), no. 3, pp. 655–701

DOI 10.4171/JEMS/211