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

• Duminil-Copin, Hugo ^[1] ; Glazman, Alexander ^[1] ; Hammond, Alan ^[2] ; Manolescu, Ioan ^[1]
  1. [1] Université de Genève

     Université de Genève

     Genève, Suiza

     
  2. [2] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 2, 2016, págs. 955-983
• Idioma: inglés
• DOI: 10.1214/14-AOP993
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• Resumen

  • 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.