The Bernoulli sieve: an overview
Alexander Gnedin, Alexander Iksanov, Alexander Marynych
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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