A random symmetric matrix with i.i.d. subgaussian entries satisfies P(rank at least n-k) at least 1-exp(-c' k n) for k up to c sqrt(n).
On subspaces spanned by random selec tions of ± 1 vectors
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On the rank of a random symmetric matrix in the large deviation regime
A random symmetric matrix with i.i.d. subgaussian entries satisfies P(rank at least n-k) at least 1-exp(-c' k n) for k up to c sqrt(n).