A binomial random family of k-subsets is the set of bases of a matroid with probability tending to 1, e^{-c^2/2}, or 0 as p = 1 - c_n / sqrt(k(n-k) binom(n,k)) with c_n tending to 0, a constant, or infinity.
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Binomial Random Matroids
A binomial random family of k-subsets is the set of bases of a matroid with probability tending to 1, e^{-c^2/2}, or 0 as p = 1 - c_n / sqrt(k(n-k) binom(n,k)) with c_n tending to 0, a constant, or infinity.