The Λ-coalescent speed of coming down from infinity
Berestycki, Julien ; Berestycki, Nathanaël ; Limic, Vlada
Ann. Probab., Tome 38 (2010) no. 1, p. 207-233 / Harvested from Project Euclid
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Consider a Λ-coalescent that comes down from infinity (meaning that it starts from a configuration containing infinitely many blocks at time 0, yet it has a finite number Nt of blocks at any positive time t>0). We exhibit a deterministic function v:(0, ∞)→(0, ∞) such that Nt/v(t)→1, almost surely, and in Lp for any p≥1, as t→0. Our approach relies on a novel martingale technique.
Publié le : 2010-01-15
Classification:  Exchangeable coalescents,  small-time asymptotics,  coming down from infinity,  martingale techniques,  fluid limits,  60J25,  60F99,  92D25 
@article{1264433997,
     author = {Berestycki, Julien and Berestycki, Nathana\"el and Limic, Vlada},
     title = {The $\Lambda$-coalescent speed of coming down from infinity},
     journal = {Ann. Probab.},
     volume = {38},
     number = {1},
     year = {2010},
     pages = { 207-233},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1264433997}
}

Berestycki, Julien; Berestycki, Nathanaël; Limic, Vlada. The Λ-coalescent speed of coming down from infinity. Ann. Probab., Tome 38 (2010) no. 1, pp.  207-233. http://gdmltest.u-ga.fr/item/1264433997/