Alexander Gnedin ; Alex Iksanov ; Uwe Roesler
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Small parts in the Bernoulli sieve
dmtcs:3567 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2008,
DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
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https://doi.org/10.46298/dmtcs.3567
Small parts in the Bernoulli sieveArticle
Authors: Alexander Gnedin 1; Alex Iksanov 2; Uwe Roesler 3
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Alexander Gnedin;Alex Iksanov;Uwe Roesler
1 Utrecht Mathematical Institute
2 Faculty of Cybernetics [Kyiv]
3 Mathematisches Seminar [Kiel]
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.
Jim Pitman;Yuri Yakubovich, 2017, Extremes and gaps in sampling from a GEM random discrete distribution, Electronic Journal of Probability, 22, none, 10.1214/17-ejp59, https://doi.org/10.1214/17-ejp59.
Alexander Iksanov, Probability and its applications, Application to the Bernoulli Sieve, 2016, 10.1007/978-3-319-49113-4_5.
Alexander Gnedin;Alexander Iksanov;Alexander Marynych, 2012, A Generalization of the Erdős–Turán Law for the Order of Random Permutation, Combinatorics, probability & computing (Print), 21, 5, pp. 715-733, 10.1017/s0963548312000247.