Bernoulli Sieve

Details Bernoulli Sieve Bernoulli Sieve

2003-03-05

arxiv.org/abs/math/0303071v1

Mathematics

Probability

16 pages

Scientific paper

Bernoulli sieve is a recursive construction of a random composition (ordered partition) of integer $n$. This composition can be induced by sampling from a random discrete distribution which has frequencies equal to the sizes of component intervals of a stick-breaking interval partition of $[0,1]$. We exploit Markov property of the composition and its renewal representation to derive asymptotics of the moments and to prove a central limit theorem for the number of parts.

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