Asymptotic laws for regenerative compositions: gamma subordinators and the like |
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Authors: | Alexander Gnedin Jim Pitman Marc Yor |
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Affiliation: | (1) Utrecht University, Utrecht, The Netherlands;(2) University of California, Berkeley, USA;(3) University of Paris VI, France |
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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 Kn of the composition when is derived from a gamma subordinator. We prove logarithmic asymptotics of the moments and central limit theorems for Kn 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+. Research supported in part by N.S.F. Grant DMS-0071448 |
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Keywords: | Primary 60G09 60C05 |
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