Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 3, pp. 495-503
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I. A. Ibragimov; N. B. Maslova. On the expected number of real zeros of random polynomials. II. Coefficients with non-zero means. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 3, pp. 495-503. http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a6/
@article{TVP_1971_16_3_a6,
author = {I. A. Ibragimov and N. B. Maslova},
title = {On the expected number of real zeros of random polynomials. {II.~Coefficients} with non-zero means},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {495--503},
year = {1971},
volume = {16},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a6/}
}
TY - JOUR
AU - I. A. Ibragimov
AU - N. B. Maslova
TI - On the expected number of real zeros of random polynomials. II. Coefficients with non-zero means
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1971
SP - 495
EP - 503
VL - 16
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a6/
LA - ru
ID - TVP_1971_16_3_a6
ER -
%0 Journal Article
%A I. A. Ibragimov
%A N. B. Maslova
%T On the expected number of real zeros of random polynomials. II. Coefficients with non-zero means
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1971
%P 495-503
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a6/
%G ru
%F TVP_1971_16_3_a6
Let $\xi_j$, $j=0,1\dots,$ be independent identically distributed random variables with $\mathbf E\xi_j\ne0$ belonging to the domain of attraction of the normal law. The main result is the following relation: $$ \mathbf E\{N_n\mid Q_n(x)\not\equiv0\}\sim\frac1\pi\ln n\quad(n\to\infty) $$ where $Q_n(x)=\sum_{j=0}^n\xi_jx^j$ and $N_n$ is the number of real roots of $Q_n$.
