Resistance in higher-dimensional Sierpiński carpets

I. McGillivray*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)


We study the effective resistance between disjoint compact sets relative to the n-th level approximation Fn to the generalized Sierpiński carpet in d dimensions. This yields a simple criterion for determining recurrence of simple random walk on the associated pre-fractal graph in terms of the resistance scaling factor.

Original languageEnglish
Pages (from-to)289-303
Number of pages15
JournalPotential Analysis
Issue number3
Publication statusPublished - 2002


  • Electrical resistance
  • Recurrence
  • Resistance scaling factor
  • Sierpinski carpets

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