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   Jorge Stolfi (jorgestolfi@mas.to)'s status on Tuesday, 12-Nov-2024 02:20:55 JST Jorge Stolfi

   Let A be an nxn matrix with random independent 0 or1 entries. What is the probability that A has zero determinant, as a function of n?

   Without thinking, I would have guessed that the probability quickly decreases with n. But for n = 1 the probability is 50%, and for n = 2, surprise, it is 10/16 = 61.5%.

   So I revised my guess to be "the probability of the determinant being zero tends to 1 as n goes to oo". 🧵>

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     Jorge Stolfi (jorgestolfi@mas.to)'s status on Tuesday, 12-Nov-2024 02:24:50 JST Jorge Stolfi

     in reply to

     🧵> But the truth is weirder! According to the paper below (pag 20) the probability for a 3x3 0-1 matrix having zero determinant is only a bit larger (~66%), but then it starts to decrease with n, being only ~45% for a 8x8 matrix...

     https://arxiv.org/pdf/math/0511636