{"id":"openai-math/The-sharp-exponential-rate-of-singularity-for-symmetric-Bernoulli-matrices","pdf":"https://github.com/openai/math/blob/main/preprints/The-sharp-exponential-rate-of-singularity-for-symmetric-Bernoulli-matrices-October-3-2026/symmetric-bernoulli-singularity.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-sharp-exponential-rate-of-singularity-for-symmetric-Bernoulli-matrices-October-3-2026","tags":["random-matrices","probability","combinatorics"],"score":0,"title":"The sharp exponential rate of singularity for symmetric Bernoulli matrices","domain":"Probability and statistical mechanics","family":"239","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"Let A n be a symmetric $`n\\times n`$ matrix whose entries on and above the diagonal are independent uniform signs. We prove $`\\displaystyle \\Pr(\\det A_n=0)=\\left(\\frac12+o(1)\\right)^n.`$","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-03","reactions":{},"formalized":false,"family_title":"Sharp singularity rates for symmetric random sign matrices"}