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The sharp exponential rate of singularity for symmetric Bernoulli matrices

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OpenAI Mathopenai-math/The-sharp-exponential-rate-of-singularity-for-symmetric-Bernoulli-matricesOct 3, 2026math.PRAI-generatedscore 0

Let A n be a symmetric $n\times n$ matrix whose entries on and above the diagonal are independent uniform signs. We prove $\displaystyle \Pr(\det A_n=0)=\left(\frac12+o(1)\right)^n.$

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