## Asymptotic laws for compositions derived from transformed subordinators.(English)Zbl 1142.60327

Summary: A random composition of $$n$$ appears when the points of a random closed set $$\widetilde{\mathcal R}\subset[0,1]$$ are used to separate into blocks $$n$$ points sampled from the uniform distribution. We study the number of parts $$K_n$$ of this composition and other related functionals under the assumption that $$\widetilde{\mathcal R}=\phi(S_{\bullet})$$, where $$(S_t$$, $$t\geq 0)$$ is a subordinator and $$\phi: [0,\infty]\to[0,1]$$ is a diffeomorphism. We derive the asymptotics of Kn when the Lévy measure of the subordinator is regularly varying at 0 with positive index. Specializing to the case of exponential function $$\phi(x)=1-e^{-x}$$, we establish a connection between the asymptotics of $$K_n$$ and the exponential functional of the subordinator.

### MSC:

 60G09 Exchangeability for stochastic processes 60C05 Combinatorial probability
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### References:

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