DMTCS Proceedings, Fifth Colloquium on Mathematics and Computer Science

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Small parts in the Bernoulli sieve

Alexander Gnedin, Alex Iksanov, Uwe Roesler


Sampling from a random discrete distribution induced by a `stick-breaking' process is considered. Under a moment condition, it is shown that the asymptotics of the sequence of occupancy numbers, and of the small-parts counts (singletons, doubletons, etc) can be read off from a limiting model involving a unit Poisson point process and a self-similar renewal process on the half-line.

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