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arXiv · 1005.5705

The Bernoulli sieve: an overview

Alexander Gnedin·Alexander Iksanov·Alexander Marynych
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Abstract

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.

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Alexander Gnedin, Alexander Iksanov, Alexander Marynych. 2010-05-31. The Bernoulli sieve: an overview. https://arxiv.org/abs/1005.5705

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