Alexander Gnedin ; Alex Iksanov ; Uwe Roesler - 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 - https://doi.org/10.46298/dmtcs.3567
Small parts in the Bernoulli sieveArticle

Authors: Alexander Gnedin 1; Alex Iksanov 2; Uwe Roesler 3

  • 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.

https://doi.org/10.46298/dmtcs.3567
Source: HAL:hal-01194688v1
Volume: DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: random occupancy scheme,multiplicative renewal process,Poisson process,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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