On nested infinite occupancy scheme in random environment

2018/08/01 by Alexander Gnedin, Gnedin, Alexander, Alexander Iksanov +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1808.00538

27 pages, several errors have been corrected; a new section on the Poisson-Kingman model has been added

arxiv created 2018/11/28 · arxiv updated 2018/11/29

Abstract

We consider an infinite balls-in-boxes occupancy scheme with boxes organised in nested hierarchy, and random probabilities of boxes defined in terms of iterated fragmentation of a unit mass. We obtain a multivariate functional limit theorem for the cumulative occupancy counts as the number of balls approaches infinity. In the case of fragmentation driven by a homogeneous residual allocation model our result generalises the functional central limit theorem for the block counts in Ewens' and more general regenerative partitions.

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