Random walks in Euclidean space

• 成果类型: Article
• 署名作者: Varju, Peter Pal
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2015.181.1.4
• 发表日期: 2015
• 页码: 243-301
• 关键词: CENTRAL-LIMIT-THEOREM; spectral gap; MOTIONS; EXTENSIONS

摘要

Fix a probability measure on the space of isometrics of Euclidean space R-d. Let Y-0 = 0, Y-1, Y-2,... is an element of R-d be a sequence of random points such that Yl+1 is the image of Yi under a random isomrnetry of the previously fixed probability law, which is independent of Y-l. We prove a Local Limit Theoremrn for Y-l under necessary nondcgeneracy conditions. Moreover, under more restrictive but still general conditions we give a quantitative estimate which describes the behavior of the law of Y-l on scales e(-cl 1/4) < r < l(1/2)