Regeneration in random combinatorial structures

A.V. Gnedin

    Research output: Contribution to journalArticleAcademicpeer-review

    Abstract

    Kingman’s theory of partition structures relates, via a natural sampling procedure, finite partitions to hypothetical infinite populations. Explicit formulas for distributions of such partitions are rare, the most no- table exception being the Ewens sampling formula, and its two-parameter extension by Pitman. When one adds an extra structure to the partitions like a linear order on the set of blocks and regenerative properties, some representation theorems allow to get more precise information on the dis- tribution. In these notes we survey recent developments of the theory of regenerative partitions and compositions. In particular, we discuss connec- tion between ordered and unordered structures, regenerative properties of the Ewens-Pitman partitions, and asymptotics of the number of compo- nents.
    Original languageEnglish
    Pages (from-to)105-156
    Number of pages52
    JournalProbability Surveys
    Volume7
    DOIs
    Publication statusPublished - 2010

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