Two random walks on upper triangular matrices (Q5937289)

The author investigates the convergence of two kinds of random walks on the groups \(U(n,\mathbb{F}_q)\) of upper triangular matrices over the finite fields \(\mathbb{F}_q\) for large dimensions \(n\). In particular, upper bounds for the rates of convergence to the uniform distribution are given with respect to the total variation norm. Proofs depend on clever applications of the relations between these distances and strong uniform stopping times. The results in the paper improve estimates of R. Stong, but the precise rates of convergence still remain unclear.