Compound random mappings

Jennie C. Hansen, Jerzy Jaworski

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we introduce a compound random mapping model which can be viewed as a generalization of the basic random mapping model considered by Ross and by Jaworski. We investigate a particular example, the Poisson compound random mapping, and compare results for this model with results known for the well-studied uniform random mapping model. We show that, although the structure of the components of the random digraph associated with a Poisson compound mapping differs from the structure of the components of the random digraph associated with the uniform model, the limiting distribution of the normalized order statistics for the sizes of the components is the same as in the uniform case, i.e. the limiting distribution is the Poisson-Dirichlet(1/2) distribution on the simplex {{xi}: Sxi = 1, xi = xi + 1 = 0 for every i = 1}.

Original languageEnglish
Pages (from-to)712-729
Number of pages18
JournalJournal of Applied Probability
Volume39
Issue number4
DOIs
Publication statusPublished - Dec 2002

Keywords

  • Component structure
  • Poisson-Dirichlet distribution
  • Random mappings

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