CAPACITY OF THE RANGE OF RANDOM WALK ON Z4

• 成果类型: Article
• 署名作者: Asselah, Amine; Schapira, Bruno; Sousi, Perla
• 署名单位: Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1288
• 发表日期: 2019
• 页码: 1447-1497
• 关键词: intersection-properties; brownian paths; Invariance; exponents

摘要

We study the scaling limit of the capacity of the range of a random walk on the integer lattice in dimension four. We establish a strong law of large numbers and a central limit theorem with a non-Gaussian limit. The asymptotic behaviour is analogous to that found by Le Gall in '86 [Comm. Math. Phys. 104 (1986) 471-507] for the volume of the range in dimension two.