 Continuity and weak convergence of ranked and size-biased permutations on the infinite simplexPeter Donnelly and Paul Joyce Stochastic Processes and their Applications, 1989, vol. 31, issue 1, 89-103 Abstract: Ranked and size-biased permutations are particular functions on the set of probability measures on the simplex. They represent two recently studied schemes for relabelling groups in certain stochastic models, and are of particular interest in describing the limiting behaviour of such models. We prove that the ranked permutations of a sequence of measures converge if and only if the size-biased permutations converge, and give conditions under which weak convergence of measures guarantees weak convergence of both permutations. Applications include a proof of the fact that the GEM distribution is the size biased permutation of the Poisson-Dirichlet and a new proof of the fact that when labelled in a particular way, normalized cycle lengths in a random permutation converge to the GEM distribution. These techniques also allow some problems concerned with the random splitting of an interval to be related to known results in other fields. Keywords: ranking; function; exchangeability; random; permutations; random; splitting; GEM; distribution; Poisson-Dirichlet; distribution (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:31:y:1989:i:1:p:89-103 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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