%0 Journal Article
%T Self-avoiding walk is sub-ballistic
%A Hugo Duminil-Copin
%A Alan Hammond
%J Mathematics
%D 2012
%I arXiv
%R 10.1007/s00220-013-1811-1
%X We prove that self-avoiding walk on Z^d is sub-ballistic in any dimension d at least two. That is, writing ||u|| for the Euclidean norm of u \in Z^d, and SAW_n for the uniform measure on self-avoiding walks gamma:{0,...,n} \to Z^d for which gamma_0 = 0, we show that, for each v > 0, there exists c > 0 such that, for each positive integer n, SAW_n (max {|| gamma_k || : k \in {0,...,n}} > v n) < e^{- c n}.
%U http://arxiv.org/abs/1205.0401v1