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

Hugo Duminil-Copin, Alexander Glazman, Martin T. Barlow, Ioan Manolescu

• We prove two results on the delocalization of the endpoint of a uniform self-avoiding walk on Zd for d≥2. 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, when x is fixed, with ∥x∥=1, this probability decreases faster than n−1/4+ε for any ε>0. This provides a bound on the probability that a self-avoiding walk is a polygon.