Random Kac polynomials have discriminant |Δ(f_n)| = n^{2n} e^{-D_* n(1+o(1))} with an explicit universal constant D_* ≈ 5.92947.
Bary-Soroker and G
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Law of large numbers for the discriminant of random polynomials
Random Kac polynomials have discriminant |Δ(f_n)| = n^{2n} e^{-D_* n(1+o(1))} with an explicit universal constant D_* ≈ 5.92947.