ON THE PROBABILITY THAT SELF-AVOIDING WALK ENDS AT A GIVEN POINT

• 成果类型: Article
• 署名作者: Duminil-Copin, Hugo; Glazman, Alexander; Hammond, Alan; Manolescu, Ioan
• 署名单位: University of Geneva; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP993
• 发表日期: 2016
• 页码: 955-983
• 关键词: connective constant; critical-behavior; dimensions; number; models

摘要

We prove two results on the delocalization of the endpoint of a uniform self-avoiding walk on Z(d) 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 parallel to x parallel to = 1, this probability decreases faster than n(-1/4+epsilon) for any epsilon > 0. This provides a bound on the probability that a self-avoiding walk is a polygon.