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erdos_522.variants.number_real_roots

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Erdős and Offord showed that the number of real roots of a random degree `n` polynomial with `±1` coefficients is `(2/π+o(1))log n`.

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Lean 4 Statement 
theorem erdos_522.variants.number_real_roots : ∃ p o : ℕ → ℝ,
    Filter.Tendsto o Filter.atTop (𝓝 0) ∧ Filter.Tendsto p Filter.atTop (𝓝 0) ∧
    ∀ (Ω : Type*) [MeasureSpace Ω] [IsProbabilityMeasure (ℙ : Measure Ω)]
      (n : ℕ) (hn : 2 ≤ n) (f : KacPolynomial n ({-1, 1} : Set ℝ) Ω),
      (ℙ {ω | |(f.roots ω).card / (n : ℝ).log - 2 / π| ≥ o n}).toReal ≤ p n
ID: ErdosProblems__522__erdos_522.variants.number_real_roots
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