Cut-off phenomenon for the ax+b Markov chain over a finite field

Emmanuel Breuillard, Péter P. Varjú

We study the Markov chain $x_{n+1}=a{x}_n+b_n$ on a finite field ${\mathbb{F}}_p$, where $a\in {\mathbb{F}}_p$ is fixed and $b_n$ are independent and identically distributed random vari…