Mixing time of fractional random walk on finite fields

Jimmy He, Huy Tuan Pham, Max Wenqiang Xu

We study a random walk on ${\mathbb{F}}_p$ defined by $X_{n+1}=1/X_n+{\epsilon }_{n+1}$ if $X_n\ne 0$, and $X_{n+1}={\epsilon }_{n+1}$ if $X_n=0$, where ${\epsilon }_{n+1}$ are inde…