Determines the sharp exponential singularity rate of symmetric random sign matrices with independent entries on and above the diagonal. Uniform signs give \(\Pr(\det A_n=0)=(1/2+o(1))^n\); for fixed bias \(p\in(0,1)\setminus\{1/2\}\), the rate is \((p^2+(1-p)^2+o(1))^n\). In the biased case, agreeing rows attain this rate.
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In The sharp exponential rate of singularity for symmetric Bernoulli matrices, 3 October 2026
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For the symmetric Bernoulli matrix A_n,
In The sharp singularity rate for biased symmetric sign matrices, 4 October 2026
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For every fixed p\in(0,1)\setminus\{1/2\},
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Why this passage is shown
Theorem 1.1
In The sharp exponential rate of singularity for symmetric Bernoulli matrices, 3 October 2026
Why this passage is shown
Theorem 1.1
In The sharp singularity rate for biased symmetric sign matrices, 4 October 2026