Rank deficiency of random matrices


Abstract in English

Let $M_n$ be a random $ntimes n$ matrix with i.i.d. $text{Bernoulli}(1/2)$ entries. We show that for fixed $kge 1$, [lim_{nto infty}frac{1}{n}log_2mathbb{P}[text{corank }M_nge k] = -k.]

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