Rassal polinomların reel köklerinin istatistikleri

In this thesis, we present two approaches in order to study the expected number of real zeros of random univariate polynomials. Namely, the Kac-Rice method and Edelman-Kostlan's geometric approach. We derive a remarkable result called the Kac-Rice formula concerning the expected number of real zeros and apply this result to certain random polynomial ensembles. We also report some basic facts from potential theory in the complex plane and its connection with complex random polynomials. In addition, we consider a class of random orthogonal polynomials associated with suitable weight functions supported in the complex plane, and we present some known statistical results in this direction.