A representation of random matrices in orispherical coordinates and its application to telegraph equations

A central limit theorem for products $g(n)=g_1g_2\dots g_n$ of random matrices $g_1,g_2,\dots,g_n$ was considered in an earlier paper [5], a representation
$$ g(n)=x(n)d(n)u(n) $$
with orthogonal (unitary) matrices $x(n)$ and $u(n)$ and diagonal $d(n)$ being investigated. Products of random matrices, as far as we know, arise in the theory of telegraph equations [9], [10], where the matrices $g_1,\dots,g_n$ are symplectic, but unitary matrices have no immediate physical interpretation in the frame of this theory. From the viewpoint of possible applications a more physical form of central limit theorem is highly desirable. Such forms are given in the present paper.