The Bernoulli sieve is a recursive construction of a random composition (ordered partition) of an integer n. This composition can be induced by sampling from a random discrete distribution which has frequencies equal to the sizes of components of a stick-breaking interval partition of [0,1]. We exploit the Markov property of the composition and its renewal representation to study the number of its parts. We derive asymptotics of the moments and prove a central limit theorem.
"The Bernoulli sieve." Bernoulli 10 (1) 79 - 96, February 2004. https://doi.org/10.3150/bj/1077544604