Discrete wave equations with random parameters and a discrete string with random masses

The problem under consideration is a modern development of one of the oldest problems of mathematics and mechanics: investigating oscillations of a string, the mass of which is concentrated in a finite number of equidistant points for the case where the masses are realizations of a sequence of random variables. By studying the corresponding differential equation with random parameters, explicit asymptotic expressions are obtained for frequencies and amplitudes of random oscillations and their probabilistic characteristics for a finite string and in which the number of points tends to infinity. Central limit theorems are established for functions characterizing frequencies of oscillations.