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  1. Home > Articles & Issues >
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  3. Small parts in the B ...
Conference paper

Small parts in the Bernoulli sieve

Alexander Gnedin (1), Alex Iksanov (2), Uwe Roesler (3)
(1) Utrecht Mathematical Institute
(2) Faculty of Cybernetics [Kyiv]
(3) Mathematisches Seminar [Kiel]
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Imported on
May 10, 2017
Published on
December 31, 2007
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
Proceedings
DOI
10.46298/dmtcs.3567
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https://about.hal.science/hal-authorisation-v1
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Small parts in the Bernoulli sieve

Alexander Gnedin (1), Alex Iksanov (2), Uwe Roesler (3)
(1) Utrecht Mathematical Institute
(2) Faculty of Cybernetics [Kyiv]
(3) Mathematisches Seminar [Kiel]
Abstract
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.
Keywords
  • [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]
  • Poisson process
  • multiplicative renewal process
  • random occupancy scheme
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