Abstract
A new method is proposed for proving some theorems on the convergence of sequences of random quantities ξ 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 ξ 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.
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 44– 65, November–December 2004.
Part 1 was published in Cybernetics and Systems Analysis, No. 5, 2004.
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Alekseichuk, A.N. A probabilistic scheme of independent random elements distributed over a finite lattice. II. The method of lattice moments. Cybern Syst Anal 40, 824–841 (2004). https://doi.org/10.1007/s10559-005-0022-y
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DOI: https://doi.org/10.1007/s10559-005-0022-y