Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 229-248
Citer cet article
I. A. Ibragimov. On the expected number of real zeros of random polynomials I. Coefficients with zero means. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 229-248. http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a2/
@article{TVP_1971_16_2_a2,
author = {I. A. Ibragimov},
title = {On the expected number of real zeros of random polynomials {I.~Coefficients} with zero means},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {229--248},
year = {1971},
volume = {16},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a2/}
}
TY - JOUR
AU - I. A. Ibragimov
TI - On the expected number of real zeros of random polynomials I. Coefficients with zero means
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1971
SP - 229
EP - 248
VL - 16
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a2/
LA - ru
ID - TVP_1971_16_2_a2
ER -
%0 Journal Article
%A I. A. Ibragimov
%T On the expected number of real zeros of random polynomials I. Coefficients with zero means
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1971
%P 229-248
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%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a2/
%G ru
%F TVP_1971_16_2_a2
Let $\xi_j$, $j=0,1,\dots$, be independent identically distributed random variables with $\mathbf E\xi_j=0$ and belong to the domain of attraction of the normal law. The main result is: $$ \mathbf E\{N_n\mid Q_n(x)\not\equiv0\}\underset{n\to\infty}\sim\frac2\pi\ln n\quad\text{if }\mathbf P\{\xi_j\ne0\}>0 $$ where $Q_n(x)=\sum_{j=0}^n\xi_jx^j$, $N_n$ is the number of real roots of $Q_n$.
