1305.1257 (Hugo Duminil-Copin et al.)

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

Hugo Duminil-Copin, Alexander Glazman, Alan Hammond, Ioan Manolescu

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.

View original: http://arxiv.org/abs/1305.1257