M ar 2 00 4 Asymptotic laws for compositions derived from transformed subordinators ∗

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 K n of this composition and other related functionals under the assumption that R = φ(S t) where (S t , t ≥ 0) is a subordinator and φ : [0, ∞] → [0, 1] is a diffeomorphism. We derive the asymptotics of K n for the case when the Lévy measure of 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 of the asymptotics of K n to the exponential functional of subordinator.