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The Bernoulli sieve: an overview

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. The Bernoulli sieve: an overview. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. pp.329-342, ⟨10.46298/dmtcs.2770⟩. ⟨hal-01185568⟩



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