Distribution of the combinatorial multisets component vectors

Eugenijus Manstavičius, Robertas Petuchovas
2012 Lietuvos matematikos rinkinys  
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
more » ... in result is an estimate of the total variation distance.
doi:10.15388/lmr.a.2012.12 fatcat:2ckbk3krwjhktcxbho6sk5mvou