. PR ] 2 3 Fe b 20 05 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 •) where (S t , t ≥ 0) is a subordinator and φ : [0, ∞] → [0, 1] is a diffeomorphism. We derive the asymptotics of K n 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 K n and the exponential functional of the subordinator.