%0 Journal Article
%T The Bernoulli sieve: an overview
%A Alexander Gnedin
%A Alexander Iksanov
%A Alexander Marynych
%J Mathematics
%D 2010
%I arXiv
%X The Bernoulli sieve is a version of the classical balls-in-boxes occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative random walk, also known as the residual allocation model or stick-breaking. We give an overview of the limit theorems concerning the number of boxes occupied by some balls out of the first $n$ balls thrown, and present some new results concerning the number of empty boxes within the occupancy range.
%U http://arxiv.org/abs/1005.5705v1