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Asymptotic laws for regenerative compositions: gamma subordinators and the like. (English) Zbl 1099.60023

The random exponentially transfomed set in the interval \([0,1]\) generated by a Gamma subordinator generates clusters for \(n\) uniform random points in \([0,1]\). The authors prove a central limit theorem for the number \(K_n\) of components. The proof is based on the contraction method for the degenerate case of R. Neininger and the reviewer [Ann. Probab. 32, No. 3B, 2838–2856 (2004; Zbl 1060.60005)]. The paper complements previous work of the authors for the case that the tail of the Lévy measure is regularly varying at \(0\).

MSC:

60G09 Exchangeability for stochastic processes
60C05 Combinatorial probability

Citations:

Zbl 1060.60005
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References:

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