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 Mat. Vopr. Kriptogr., 2012, Volume 3, Issue 2, Pages 63–78 (Mi mvk54)

Poisson approximation for the distribution of the number of “parallelograms” in a random sample from $\mathbb Z_N^q$

V. I. Kruglov

Steklov Mathematical Institute of RAS, Moscow

Abstract: For a random sample with replacement $\xi_1,…,\xi_T$ from a group $\mathbb Z_N^q$, $N\geq4$, we consider the distribution of the number $\zeta$ of 4-element subsets satisfying the relation of type $\xi_{i_1}-\xi_{i_2}=\xi_{i_3}-\xi_{i_4}$ and additional condition given in terms of a metric on this group. Estimates of the accuracy of Poisson approximation for the distribution of $\zeta$ are obtained and conditions of the weak convergence of $\zeta$ to the Poisson law are established.

Key words: random elements of a group, coincidence of differences, Poisson approximation.

DOI: https://doi.org/10.4213/mvk54

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UDC: 519.212.2+519.214

Citation: V. I. Kruglov, “Poisson approximation for the distribution of the number of “parallelograms” in a random sample from $\mathbb Z_N^q$”, Mat. Vopr. Kriptogr., 3:2 (2012), 63–78

Citation in format AMSBIB
\Bibitem{Kru12} \by V.~I.~Kruglov \paper Poisson approximation for the distribution of the number of parallelograms'' in a~random sample from $\mathbb Z_N^q$ \jour Mat. Vopr. Kriptogr. \yr 2012 \vol 3 \issue 2 \pages 63--78 \mathnet{http://mi.mathnet.ru/mvk54} \crossref{https://doi.org/10.4213/mvk54}