Signed random combinatorial matrices with exactly n/2 zeros per row have smallest singular value at least order 1/sqrt(n) with probability 1 minus O(ε) minus exp(-cn).
Estimates for the concentration function of combinatorial number theory and probability
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The smallest singular value of signed random combinatorial matrices
Signed random combinatorial matrices with exactly n/2 zeros per row have smallest singular value at least order 1/sqrt(n) with probability 1 minus O(ε) minus exp(-cn).