A random process related to a random walk on upper triangular matrices over a finite field

Abstract

Abstract This article considers a random process related to a random walk on n by n upper triangular matrices over a finite field F q where q is an odd prime. The walk starts with the identity, and at each step, i is selected at random from { 2 , … , n } and either row i or the negative of row i is added to row i − 1 . This article shows that, for a given q , it takes order n 2 steps for the last column to get close to uniformly distributed over all possibilities for that column.