Generating Random Elements in SLn (Fq) by Random Transvections

Abstract. This paper studies a random walk based on random transvections in SLn(Fq,) and shows that, given 6 > 0, there is a constant c such that after n + c steps the walk is within a distance e from uniform and that after nc steps the walk is a distance at least 1 e from uniform. This paper uses results of Diaconis and Shahshahani to get the upper bound, uses results of Rudvalis to get the lower bound, and briefly considers some other random walks on SLn(Fq) to compare them with random transvections.