Abstract:
Let ξj, j=0,1,…, be independent identically distributed random variables with Eξj=0 and belong to the domain of attraction of the normal law.
The main result is:
E{Nn∣Qn(x)≢0}∼n→∞2πlnnif P{ξj≠0}>0
where Qn(x)=∑nj=0ξjxj, Nn is the number of real roots of Qn.
Citation:
I. A. Ibragimov, “On the expected number of real zeros of random polynomials I. Coefficients with zero means”, Teor. Veroyatnost. i Primenen., 16:2 (1971), 229–248; Theory Probab. Appl., 16:2 (1971), 228–248
\Bibitem{Ibr71}
\by I.~A.~Ibragimov
\paper On the expected number of real zeros of random polynomials I.~Coefficients with zero means
\jour Teor. Veroyatnost. i Primenen.
\yr 1971
\vol 16
\issue 2
\pages 229--248
\mathnet{http://mi.mathnet.ru/tvp2144}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=286157}
\zmath{https://zbmath.org/?q=an:0277.60051}
\transl
\jour Theory Probab. Appl.
\yr 1971
\vol 16
\issue 2
\pages 228--248
\crossref{https://doi.org/10.1137/1116023}
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