Abstract
For a random closed set obtained by exponential transformation of the closed range of a subordinator, a regenerative composition of generic positive integer n is defined by recording the sizes of clusters of n uniform random points as they are separated by the points of . We focus on the number of parts K n of the composition when is derived from a gamma subordinator. We prove logarithmic asymptotics of the moments and central limit theorems for K n and other functionals of the composition such as the number of singletons, doubletons, etc. This study complements our previous work on asymptotics of these functionals when the tail of the Lévy measure is regularly varying at 0+.
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Research supported in part by N.S.F. Grant DMS-0071448
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Gnedin, A., Pitman, J. & Yor, M. Asymptotic laws for regenerative compositions: gamma subordinators and the like. Probab. Theory Relat. Fields 135, 576–602 (2006). https://doi.org/10.1007/s00440-005-0473-0
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DOI: https://doi.org/10.1007/s00440-005-0473-0