Almost sure functional central limit theorem for the linear random walk on the torus

• 成果类型: Article
• 署名作者: Boyer, Jean-Baptiste
• 署名单位: Universite Paris Saclay
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0871-8
• 发表日期: 2019
• 页码: 651-696
• 关键词: stationary measures

摘要

Let be a probability measure on :=SLd(Z). Consider the random walk defined by on the torus Td=Rd/Zd: for any xTd, the walk starting at x is defined by where (gn)N is chosen with the law circle times N. Bourgain, Furmann, Lindenstrauss and Mozes proved that under an assumption on the group generated by the support of , the random walk starting at any irrational point equidistributes in the torus. In this article, we study the Functional Central Limit Theorem and the almost sure Functional Central Limit Theorem for this walk starting at some points having good diophantine properties.