Asymptotically one-dimensional diffusions on the Sierpinski gasket and the abc-gaskets

Kumiko Hattori, Tetsuya Hattori, Hiroshi Watanabe

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

Diffusion processes on the Sierpinski gasket and the abc-gaskets are constructed as limits of random walks. In terms of the associated renormalization group, the present method uses the inverse trajectories which converge to unstable fixed points corresponding to the random walks on one-dimensional chains. In particular, non-degenerate fixed points are unnecessary for the construction. A limit theorem related to the discrete-time multi-type non-stationary branching processes is applied.

Original languageEnglish
Pages (from-to)85-116
Number of pages32
JournalProbability Theory and Related Fields
Volume100
Issue number1
DOIs
Publication statusPublished - 1994 Mar 1
Externally publishedYes

Keywords

  • Mathematics Subject Classification: 60J60, 60J25, 60J85, 60J15

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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