On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a~random sequence
Diskretnaya Matematika, Tome 20 (2008) no. 4, pp. 113-119
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In a long enough sequence of discrete random variables, as a rule, an $s$-tuple exists of nontrivial structure, that is, a tuple with at least one repeated symbol. We consider the case where the sequence consists of $n+s-1$ independent random variables taking the values $1,\dots,N$ with equal probabilities. It is shown that as $n\to\infty$, $ns^3N^{-2}\to0$ the probability of that in the sequence $s$-tuples exist with the same nontrivial structure is equal to $1-(1+n/N)^se^{-sn/N}(1+o(1))$.
@article{DM_2008_20_4_a9,
author = {V. G. Mikhailov},
title = {On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a~random sequence},
journal = {Diskretnaya Matematika},
pages = {113--119},
publisher = {mathdoc},
volume = {20},
number = {4},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_2008_20_4_a9/}
}
TY - JOUR AU - V. G. Mikhailov TI - On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a~random sequence JO - Diskretnaya Matematika PY - 2008 SP - 113 EP - 119 VL - 20 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DM_2008_20_4_a9/ LA - ru ID - DM_2008_20_4_a9 ER -
%0 Journal Article %A V. G. Mikhailov %T On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a~random sequence %J Diskretnaya Matematika %D 2008 %P 113-119 %V 20 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/DM_2008_20_4_a9/ %G ru %F DM_2008_20_4_a9
V. G. Mikhailov. On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a~random sequence. Diskretnaya Matematika, Tome 20 (2008) no. 4, pp. 113-119. http://geodesic.mathdoc.fr/item/DM_2008_20_4_a9/