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 sieveConference paper

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: [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], [en] Poisson process, multiplicative renewal process, random occupancy scheme

6 Documents citing this article

Share and export

Consultation statistics

This page has been seen 687 times.
This article's PDF has been downloaded 325 times.