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Erdős problem 521

Let (ϵk)k≥0(\epsilon_k)_{k\geq 0} be independently uniformly chosen at random from {−1,1}\{-1,1\}. If RnR_n counts the number of real roots of fn(z)=∑0≤k≤nϵkzkf_n(z)=\sum_{0\leq k\leq n}\epsilon_k z^k then is it true that, almost surely, lim⁡n→∞Rnlog⁡n=2π?\lim_{n\to \infty}\frac{R_n}{\log n}=\frac{2}{\pi}?

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3 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

521.lean

Retained formal statement3 of 3

fairCoin is a probability measure.

FormalConjectures/ErdosProblems/521.leanErdos521.fairCoin_isProbabilityMeasure1 lineExact file
MeasureTheory.IsProbabilityMeasure Erdos521.fairCoin
APIStatement only, no proofformal statement reference