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Teoriya Veroyatnostei i ee Primeneniya, 1974, Volume 19, Issue 3, Pages 488–500
(Mi tvp2922)
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This article is cited in 20 scientific papers (total in 20 papers)
On the distribution of the number of real roots of random polynomials
N. B. Maslova Leningrad
Abstract:
Let $\xi_0,\xi_1,\dots$ be a sequence of independent identically distributed random variables and $N$ be the number of real roots of the polynomial
$$
Q(x)=\sum_{j=0}^n\xi_jx^j.
$$
The main result is the following
Theorem. {\it If $\mathbf P\{\xi_j=0\}=0$, $\mathbf E\xi_j=0$ and $\mathbf E|\xi_j|^{2+s}<\infty$ for some positive number $s$, then, for any real} $t$,
$$
\mathbf E\exp\{it(N-\mathbf EN)(\mathbf DN)^{-1/2}\}\underset{n\to\infty}\longrightarrow е^{-t^2/2}.
$$
Received: 28.09.1972
Citation:
N. B. Maslova, “On the distribution of the number of real roots of random polynomials”, Teor. Veroyatnost. i Primenen., 19:3 (1974), 488–500; Theory Probab. Appl., 19:3 (1975), 461–473
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