Uniqueness of Brownian motion on Sierpiński carpets

Martin T. Barlow, Richard F. Bass, Takashi Kumagai, Alexander Teplyaev

Research output: Contribution to journalArticlepeer-review

74 Citations (Scopus)


We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpiński 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.

Original languageEnglish
Pages (from-to)655-701
Number of pages47
JournalJournal of the European Mathematical Society
Issue number3
Publication statusPublished - 2010
Externally publishedYes


  • Brownian motion
  • Diffusions
  • Dirichlet forms
  • Fractals
  • Sierpiński carpet
  • Uniqueness

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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