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On the probability that self-avoiding walk ends at a given point

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Year 2013
Abstract We prove two results on the delocalization of the endpoint of a uniform self-avoiding walk on Z^d for d>1. We show that the probability that a walk of length n ends at a point x tends to 0 as n tends to infinity, uniformly in x. Also, for any fixed x in Z^d, this probability decreases faster than n^{-1/4 + epsilon} for any epsilon >0. When |x|= 1, we thus obtain a bound on the probability that self-avoiding walk is a polygon.
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arXiv: 1305.1257
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DUMINIL-COPIN, Hugo et al. On the probability that self-avoiding walk ends at a given point. 2013. https://archive-ouverte.unige.ch/unige:30543

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Deposited on : 2013-10-21

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