Cut-off phenomenon for the ax plus b Markov chain over a finite field
成果类型：
Article
署名作者：
Breuillard, Emmanuel; Varju, Peter P.
署名单位：
University of Oxford; University of Cambridge
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-022-01161-w
发表日期：
2022
页码：
85-113
关键词：
摘要：
We study the Markov chain x(n+1 )= ax(n) + b(n) on a finite field F-p, where a is an element of F-p(x) is fixed and b(n) are independent and identically distributed random variables in F-p. Conditionally on the Riemann hypothesis for all Dedekind zeta functions, we show that the chain exhibits a cut-off phenomenon for most primes p and most values of a is an element of F-p(x). We also obtain weaker, but unconditional, upper bounds for the mixing time.
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