Distribution of the combinatorial multisets component vectors
Articles
Eugenijus Manstavičius
Vilnius University
Robertas Petuchovas
Vilnius University
Published 2012-12-15
https://doi.org/10.15388/LMR.A.2012.12
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Keywords

Random combinatorial multiset
negative binomial distribution
additive function
central limit theorem

How to Cite

Manstavičius, E. and Petuchovas, R. (2012) “Distribution of the combinatorial multisets component vectors”, Lietuvos matematikos rinkinys, 53(A), pp. 66–71. doi:10.15388/LMR.A.2012.12.

Abstract

We explore a class of random combinatorial structures called weighted multisets. Their components are taken from an initial set satisfying general boundedness conditions posed on the number of elements with a given weight. The component vector of a multiset of weight n taken with equal probability has dependent coordinates, nevertheless, up to r = o(n) of them as n→∞, we approximate by an appropriate vector comprised from independent negative binomial random variables. The main result is an estimate of the total variation distance.

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