2004/03/31 by Alexander Gnedin, Jim Pitman, Marc Yor · 1 citation
Mathematics · #Point processes and geometric inequalities #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60C05 #msc:60G09
paper · pdf · doi:10.1214/009117905000000639
published as Annals of Probability 2006, Vol. 34, No. 2, 468-492 · Published at http://dx.doi.org/10.1214/009117905000000639 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2006/03/01 · arxiv created 2006/05/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A random composition of n appears when the points of a random closed set ℛ̃⊂[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 ℛ̃=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. Specializing 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.