Counting intervals in the packing process

Yuliy Baryshnikov, Alexander Gnedin

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We consider a sequential interval packing process similar to Rényi's "car parking problem" but with a generator of random intervals which allows for arbitrarily small lengths. Embedding the process in continuous time, we view it as a self-similar interval splitting process. We determine the asymptotical behavior of the quantities such as the number of intervals packed to some instant and obtain convergence results in the context of the more general splitting model.

Original languageEnglish
Pages (from-to)863-877
Number of pages15
JournalAnnals of Applied Probability
Volume11
Issue number3
DOIs
Publication statusPublished - Aug 1 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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