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.Comment: 31 pages, 8 figures. Referee corrections implemented; removed section
5.