The local limit theorem on nilpotent Lie groups

• 成果类型: Article
• 署名作者: Hough, Robert
• 署名单位: State University of New York (SUNY) System; Stony Brook University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0864-7
• 发表日期: 2019
• 页码: 761-786
• 关键词: random-walks; inequalities; BEHAVIOR

摘要

A local limit theorem is proven on connected, simply connected nilpotent Lie groups, for a class of generating measures satisfying a moment condition and a condition on the characteristic function of the abelianization. The result extends an earlier local limit theorem of Alexopoulos which treated absolutely continuous measures with a continuous density of compact support, and also extends local limit theorems of Breuillard and Diaconis-Hough which treated general measures on the Heisenberg group.