Abstract
Let Q(n){x) = capital sigma (k=0)(n) be a random algebraic polynomial in which the coefficients A(0) A(1), A(2),... A(n) form a sequence of independent normally distributed random variables with mean zero. In this paper we study the case where the variances of the coefficients A(k) are increasing in k, say Var(A(k)) = e(k(2n-k)/n square root (n)), k = 0,... n. We show that the asymptotic behavior of the expected number of real zeros of Q(n)(x), in compare to the case of identically distributed coefficients, will increase to order n(1/4).