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Version 2 changes:
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-- In version 1, one inequality in Theorem 9 was wrong by a constant factor. In
   particular, it is *not* true that \|M\|_p \le \|M\|_q for p < q for a random
   matrix M (this holds in the scalar case, but not the matrix case). If M has
   rank at most r though, then it is true that \|M\|_p \le r^{1/p - 1/q} \|M\|_q.
   This appears as Lemma 5 in version 2, and this lemma is then used to correct
   the formerly incorrect inequality in the proof of Theorem 9. In the end, the
   requirement for m in Theorem 9 only changes by a constant factor. (8/25/2015)