## Asymptotic laws for compositions derived from transformed subordinators (2006)

Venue: | ANN. PROBAB |

Citations: | 23 - 10 self |

### BibTeX

@ARTICLE{Gnedin06asymptoticlaws,

author = {Alexander Gnedin and Jim Pitman and Marc Yor},

title = {Asymptotic laws for compositions derived from transformed subordinators},

journal = {ANN. PROBAB},

year = {2006},

pages = {468--492}

}

### Years of Citing Articles

### OpenURL

### Abstract

A random composition of n appears when the points of a random closed set ˜ R ⊂ [0, 1] are used to separate into blocks n points sampled from the uniform distribution. We study the number of parts Kn of this composition and other related functionals under the assumption that ˜ R = φ(S•) where (St, t ≥ 0) is a subordinator and φ: [0, ∞] → [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. Specialising to the case of exponential function φ(x) = 1 −e −x we establish a connection between the asymptotics of Kn and the exponential functional of the subordinator.