The $\Lambda$-coalescent speed of coming down from infinity

Abstract : Consider a $\Lambda$-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 $N_t$ of blocks at any positive time $t>0$). We exhibit a deterministic function $v:(0,\infty)\to (0,\infty)$, such that $N_t/v(t)\to 1$, almost surely and in $L^p$ for any $p\geq 1$, as $t\to 0$. Our approach relies on a novel martingale technique.
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Type de document :
Pré-publication, Document de travail
30 pages. 2008
Domaine :
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https://hal.archives-ouvertes.fr/hal-00321969
Contributeur : Julien Berestycki <>
Soumis le : mardi 16 septembre 2008 - 12:15:17
Dernière modification le : mercredi 29 novembre 2017 - 16:30:10

Identifiants

• HAL Id : hal-00321969, version 1
• ARXIV : 0807.4278

Citation

Julien Berestycki, Nathanael Berestycki, Vlada Limic. The $\Lambda$-coalescent speed of coming down from infinity. 30 pages. 2008. 〈hal-00321969〉

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