RANDOM WALKS DRIVEN BY LOW MOMENT MEASURES

• 成果类型: Article
• 署名作者: Bendikov, Alexander; Saloff-Coste, Laurent
• 署名单位: University of Wroclaw; Cornell University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP687
• 发表日期: 2012
• 页码: 2539-2588
• 关键词: wreath-products; markov-chains

摘要

We study the decay of convolution powers of probability measures without second moment but satisfying some weaker finite moment condition. For any locally compact unimodular group G and any positive function rho : G --> [0, +infinity], we introduce a function Phi(G,rho) which describes the fastest possible decay of n bar right arrow phi((2n)) (e) when phi is a symmetric continuous probability density such that integral rho phi is finite. We estimate Phi(G,rho) for a variety of groups G and functions rho. When rho is of the form rho = rho o delta with rho : [0, +infinity) --> [0, +infinity), a fixed increasing function, and delta : G --> [0, +infinity), a natural word length measuring the distance to the identity element in G, Phi(G,rho) can be thought of as a group invariant.