Self-avoiding walks on finite graphs of large girth

2014/02/26 by Ariel Yadin, Yadin, Ariel
Mathematics · #60K35 #82B41 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60K35 #msc:82B41

paper · pdf · doi:10.48550/arxiv.1402.6553

arxiv created 2016/06/21 · arxiv updated 2016/06/22

Abstract

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 Z^d. The expected length of a random self avoiding path is considered. 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.

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