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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
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Cybernetics and Systems Analysis Aims and scope

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.

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Authors and Affiliations

  1. Military Institute of Telecommunications and Informatization, National Technical University “Kiev Polytechnic Institute”, Kiev, Ukraine

    A. N. Alekseichuk

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  1. A. N. Alekseichuk
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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 3–15, September–October 2004.

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Alekseichuk, A.N. A probabilistic scheme of independent random elements distributed over a finite lattice. I. Exact probability distributions of functionals of union of random elements. Cybern Syst Anal 40, 629–638 (2004). https://doi.org/10.1007/s10559-005-0001-3

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  • DOI: https://doi.org/10.1007/s10559-005-0001-3

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