The Bernoulli sieve: an overview

Alexander Gnedin 1 Alexander Iksanov 2 Alexander Marynych 2
1 Mathematical Institute
2 Faculty of Cybernetics
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.
Keywords : the occupancy problem random partitions
Type de document :
Communication dans un congrès
Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.329-342, 2010, DMTCS Proceedings
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Alexander Gnedin, Alexander Iksanov, Alexander Marynych. The Bernoulli sieve: an overview. Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.329-342, 2010, DMTCS Proceedings. 〈hal-01185568〉

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