CAPACITY OF THE RANGE OF RANDOM WALK: THE LAW OF THE ITERATED LOGARITHM
成果类型：
Article
署名作者：
Dembo, Amir; Okada, Izumi
署名单位：
Stanford University; Chiba University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/24-AOP1692
发表日期：
2024
页码：
1954-1991
关键词：
摘要：
We establish both the lim sup and the lim inf law of the iterated logarithm (LIL) for the capacity of the range of a simple random walk in any dimension d >= 3. While for d >= 4, the order of growth in n of such LIL at dimension d matches that for the volume of the random walk range in dimension d - 2, somewhat surprisingly this correspondence breaks down for the capacity of the range at d = 3. We further establish such LIL for the Brownian capacity of a three-dimensional Brownian sample path and novel, sharp moderate deviations bounds for the capacity of the range of a four-dimensional simple random walk.