A probabilistic scheme of independent random elements distributed over a finite lattice. II. The method of lattice moments

Authors:
A. N. Alekseichuk
Affiliations:
Military Institute of Telecommunications and Informatization at the National Technical University "Kiev Polytechnic Institute", Kiev, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2005

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A probabilistic scheme of independent random elements distributed over a finite lattice. I. Exact probability distributions of functionals of union of random elements

Cybernetics and Systems Analysis

Works of the Kiev school of theoretical cryptography

Cybernetics and Systems Analysis

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Abstract

A new method is proposed for proving some theorems on the convergence of sequences of random quantities 驴 n that assume values in a set {0,1,...,n} to discrete probability distributions. The method is based on the investigation of definite numerical characteristics (called lattice moments) of asymptotic behavior of distributions of 驴 n and is illustrated by the examples of investigating the asymptotic behavior of the probability distribution of the solution space dimension of a system of independent random homogeneous linear equations over a finite field and that of the number of connected components of a random (unequiprobable) hypergraph with independent hyperedges.