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Bernoulli sieve is a recursive construction of a random composition (orderedpartition) of integer $n$. This composition can be induced by sampling from arandom discrete distribution which has frequencies equal to the sizes ofcomponent intervals of a stick-breaking interval partition of $[0,1]$. Weexploit Markov property of the composition and its renewal representation toderive asymptotics of the moments and to prove a central limit theorem for thenumber of parts.Comment: 16 page

A flat plane that is not the limit of periodic flat planes