The Mean Number of Real Roots for One Class of Random Polynomials

Abstract

Let $\xi_0, \xi_1, \cdots, \xi_n, \cdots$ be a Gaussian stationary sequence of random variables. We study the asymptotic behavior of the mean number of real roots of the polynomial $P_n(x) = \xi_0 + \xi_1x + \cdots + \xi_nx^n$ as $n \rightarrow \infty$.