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Supercritical self-avoiding walks are space-filling (1110.3074v3)
Published 13 Oct 2011 in math.PR, math-ph, math.CO, and math.MP
Abstract: We consider random self-avoiding walks between two points on the boundary of a finite subdomain of Zd (the probability of a self-avoiding trajectory gamma is proportional to mu{-length(gamma)}). We show that the random trajectory becomes space-filling in the scaling limit when the parameter mu is supercritical.
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