Fractal behavior in trapping and reaction: A random walk study

J. Klafter, A. Blumen, G. Zumofen

Research output: Contribution to journalArticlepeer-review


We investigate the trapping of a random walker in fractal structures (Sierpinski gaskets) with randomly distributed traps. The survival probability is determined from the number of distinct sites visited in the trap-free fractals. We show that the short-time behavior and the long-time tails of the survival probability are governed by the spectral dimension ∼d. We interpolate between these two limits by introducing a scaling law. An extension of the theory, which includes a continuous-time random walk on fractals, is discussed as well as the case of direct trapping. The latter case is shown to be governed by the fractal dimension ∼d.

Original languageEnglish
Pages (from-to)561-577
Number of pages17
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Sep 1984
Externally publishedYes


  • Sierpinski gaskets
  • Trapping
  • compact exploration
  • continuous-time random walk
  • number of distinct sites visited
  • random walk


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