Self-avoiding walks on finite graphs of large girth

Ariel Yadin
2016 Latin American Journal of Probability and Mathematical Statistics  
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 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.
doi:10.30757/alea.v13-21 fatcat:fgbil5hefrdf7obi3avzftdm6e