Geodesic
Generating random elements in $SL\sb n(F\sb q)$ by random transvections
Journal of Algebraic Combinatorics, Tome 1 (1992) no. 2, pp. 133-150.

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Summary: This paper studies a random walk based on random transvections in $SL _{n}( F _{ q })$ and shows that, given Ĩ $\in > 0$, there is a constant $c$ such that after $n + c$ steps the walk is within a distance Ĩ $\in $from uniform and that after $n - c$ steps the walk is a distance at least 1 - Ĩ $\in $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.
Keywords: transvection, random walk, representation theory, upper bound lemma 
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     title = {Generating random elements in $SL\sb n(F\sb q)$ by random transvections},
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}
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Hildebrand, Martin. Generating random elements in $SL\sb n(F\sb q)$ by random transvections. Journal of Algebraic Combinatorics, Tome 1 (1992) no. 2, pp. 133-150. http://geodesic.mathdoc.fr/item/JAC_1992__1_2_a3/