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This paper studies a random walk based on random transvections in SL n ( F q ) and shows that, given > 0, there is a constant c such that after n + c steps the walk is within a distance from uniform and that after n − c steps the walk is a distance at least 1 − 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 SL n ( F q ) to compare them with random transvections

Generating Random Elements in SL n (F q ) by Random Transvections