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

Authors:
A. N. Alekseichuk
Affiliations:
Military Institute of Telecommunications and Informatization, National Technical University "Kiev Polytechnic Institute", Kiev, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2004

Citing 3
Cited 2

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

Cybernetics and Systems Analysis
Works of the Kiev school of theoretical cryptography

Cybernetics and Systems Analysis

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Abstract

A probabilistic scheme of independent random elements with values in a finite lattice is introduced. For the scheme, exact expressions of probability distributions of a functional of general form and union of random corank elements are obtained. Various probabilistic combinatorial problems (on probability distributions of the number of uncovered points in a generalized scheme of grouped distribution of particles, on the number of connectivity components of a random hypergraph, on the number of solutions of a system of random linear equations over a finite ring with unity, etc.) are demonstrated to be naturally formulated in terms of the scheme constructed.