Geodesic
Small parts in the Bernoulli sieve
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science (2008).

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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. 
@article{DMTCS_2008_special_254_a13,
     author = {Gnedin, Alexander and Iksanov, Alex and Roesler, Uwe},
     title = {Small parts in the {Bernoulli} sieve},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science},
     year = {2008},
     doi = {10.46298/dmtcs.3567},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3567/}
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Gnedin, Alexander; Iksanov, Alex; Roesler, Uwe. Small parts in the Bernoulli sieve. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science (2008). doi : 10.46298/dmtcs.3567. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3567/

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