On Moments of Multiplicative Coalescents

Vitalii Konarovskyi (1, 2, 3) , Vlada Limic (4)

1 Universität Bielefeld = Bielefeld University
2 Institute of Mathematics of NAS of Ukraine
3 UHH - Universität Hamburg
4 IRMA - Institut de Recherche Mathématique Avancée

The motivation for this work comes from our recent paper introducing restricted multiplicative merging. In order to carry out there the scaling limit analysis, we needed an estimate of the fourth moment of the $l^2$ norm of multiplicative coalescents at any given time. In this paper, we prove existence of all the moments via a new argument, and in the process we obtain a number of related results which could be of general interest to our community. Our techniques are in part inspired by percolation, and in part are based on tools from stochastic analysis, notably the semi-martingale and the excursion theory.

Mots clés: Multiplicative coalescent; random graph; excursion; Lévy process; moment estimates

Domaines: Mathématiques [math]; Probabilités [math.PR]

Vitalii Konarovskyi, Vlada Limic. On Moments of Multiplicative Coalescents. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, In press. ⟨hal-03451100⟩