On the number of real solutions of a random polynomial
The author considers the random algebraic equation \(\sum^n_{j=0} a_jx^j= K_n\) where the coefficients \(a_j\) are independent random variables and \(K_n\) is a sequence of real numbers with suitably specified growth. He relaxes the normality assumption for coefficients by considering a general distribution with finite or infinite variance and he obtains bounds, as a function of \(n\), for the number of real solutions of the equation rather than the asymptotic value derived for the expected number of solutions in the normal case.
scientific article; zbMATH DE number 1117625
scientific article