Weakly self-avoiding walks on graphs and self-intersection events.
Preprint (Feb. 2002)

We consider the number J_n of self-intersections of a weakly self-avoiding walk with parameter ß >0 of length n on an infinite, locally finite connected transitive graph of degree > 1. We show the large deviation type result that for every fixed ß >0 there are positive finite constants b₁ < b₂ and \tau such that, for all large enough n, the probability that J_n is in [ b₁, b₂ ] exceeds 1 - e ^{- n \tau}.