Self-avoiding walks on finite graphs of large girth

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7 Scopus citations


We consider self-avoiding walk on finite graphs with large girth. We study a few aspects of the model originally considered by Lawler, Schramm and Werner on finite balls in Zd. The expected length of a random self avoiding path is considered. We discuss possible definitions of "critical" behavior in the finite volume setting. We also define a "critical exponent" γ for sequences of graphs of size tending to infinity, and show that γ= 1 in the large girth case.

Original languageEnglish
Pages (from-to)521-544
Number of pages24
Issue number2
StatePublished - 1 Jan 2016


  • Critical exponents
  • Large girth graphs
  • Self-avoiding walk

ASJC Scopus subject areas

  • Statistics and Probability


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