LARGE DEVIATION EXPANSIONS FOR THE COEFFICIENTS OF RANDOM WALKS ON THE GENERAL LINEAR GROUP

• 成果类型: Article
• 署名作者: Xiao, Hui; Grama, Ion; Liu, Quansheng
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1621
• 发表日期: 2023
• 页码: 1380-1420
• 关键词: multitype branching-process; local limit-theorem; RANDOM MATRICES; survival probability; stationary measures; PRODUCTS; CONVERGENCE; asymptotics; SUBGROUPS

摘要

Consider (gn)n>1 a sequence of independent and identically distributed random matrices and the left random walk Gn := gn . . . g1, n > 1 on the general linear group GL(d, R). Under suitable conditions we establish a Bahadur-Rao-Petrov type large deviation expansion for the coefficient (f, Gnv) of the product Gn, where v & epsilon; Rd and f & epsilon; (Rd)*. In particular, we obtain an explicit rate function in the large deviation principle, thus im-proving significantly the known large deviation bounds. A local limit theorem with large deviations for the coefficients and large deviation expansions under the change of probability measure are also proved.