Solving the problem of invariance of probabilistic characteristics for a priori solvable systems of random nonlinear equations over a finite commutative ring with unity

Abstract

A class of a priori solvable systems of random non-linear equations over a finite commutative ring with unity is considered. The questions of the bounds of the invariance domains for the limit factorial moments and, accordingly, the limit distribution of the number of solutions that are different from a fixed solution to a given system and also the geometrical structure of these solutions are investigated.