%0 Journal Article %T Small parts in the Bernoulli sieve %A Alexander Gnedin %A Alex Iksanov %A Uwe Roesler %J Mathematics %D 2008 %I arXiv %X 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 halfline. %U http://arxiv.org/abs/0804.3052v1