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230
Random recursive trees and the BolthausenSznitman coalescent
 Electron. J. Probab
, 2005
"... We describe a representation of the BolthausenSznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the coalescent restricted to [n]: we show that the distribution of the number of blocks involved in the ..."
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Cited by 34 (2 self)
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We describe a representation of the BolthausenSznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the coalescent restricted to [n]: we show that the distribution of the number of blocks involved
ON THE EXTERNAL BRANCHES OF COALESCENT PROCESSES WITH MULTIPLE COLLISIONS WITH AN EMPHASIS ON THE BOLTHAUSEN–SZNITMAN COALESCENT
, 2012
"... A recursion for the joint moments of the external branch lengths for coalescents with multiple collisions (Λcoalescents) is provided. This recursion is used to derive asymptotic expansions as the sample size n tends to infinity for the moments of the total external branch length of the Bolthausen–S ..."
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Cited by 2 (0 self)
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A recursion for the joint moments of the external branch lengths for coalescents with multiple collisions (Λcoalescents) is provided. This recursion is used to derive asymptotic expansions as the sample size n tends to infinity for the moments of the total external branch length of the Bolthausen–Sznitman
Asymptotic results about the total branch length of the BolthausenSznitman coalescent
"... We study the total branch length Ln of the BolthausenSznitman coalescent as the sample size n tends to infinity. Asymptotic expansions for the moments of Ln are presented. It is shown that Ln/E(Ln) converges to 1 in probability and that Ln, properly normalized, converges weakly to a stable random v ..."
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Cited by 6 (2 self)
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We study the total branch length Ln of the BolthausenSznitman coalescent as the sample size n tends to infinity. Asymptotic expansions for the moments of Ln are presented. It is shown that Ln/E(Ln) converges to 1 in probability and that Ln, properly normalized, converges weakly to a stable random
Total internal and external lengths of the BolthausenSznitman coalescent
, 2013
"... In this paper, we study a weak law of large numbers for the total internal length of the BolthausenSzmitman coalescent. As a consequence, we obtain the weak limit law of the centered and rescaled total external length. The latter extends results obtained by Dhersin & Möhle [9]. An application ..."
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Cited by 4 (1 self)
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In this paper, we study a weak law of large numbers for the total internal length of the BolthausenSzmitman coalescent. As a consequence, we obtain the weak limit law of the centered and rescaled total external length. The latter extends results obtained by Dhersin & Möhle [9
Asymptotics of the allele frequency spectrum associated with the BolthausenSznitman coalescent
, 2007
"... We work in the context of the infinitely many alleles model. The allelic partition associated with a coalescent process started from n individuals is obtained by placing mutations along the skeleton of the coalescent tree; for each individual, we trace back to the most recent mutation affecting it a ..."
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Cited by 14 (0 self)
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frequency spectra of the Beta(2 − α,α) coalescents with α ∈ (1,2). In this paper, we prove full asymptotics for the case of the BolthausenSznitman coalescent.
Asymptotic results concerning the total branch length of the Bolthausen–Sznitman coalescent
, 2007
"... ..."
Asymptotics of the allele frequency spectrum associated with the BolthausenSznitman coalescent
"... (joint work with AnneLaure Basdevant) We imagine a coalescent process as modelling the genealogy of a sample from a population which is subject to neutral mutation. We work under the assumptions of the infinitely many alleles model so that, in particular, every mutation gives rise to a completely n ..."
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Cited by 1 (0 self)
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(joint work with AnneLaure Basdevant) We imagine a coalescent process as modelling the genealogy of a sample from a population which is subject to neutral mutation. We work under the assumptions of the infinitely many alleles model so that, in particular, every mutation gives rise to a completely
Abstracts Cutting random recursive trees, and the Bolthausen–Sznitman
"... The Bolthausen–Sznitman coalescent was introduced in the context of spin glasses in [1]. These days, it is usually thought of as a special case of a more general class of coalescent processes introduced by Pitman [5] and Sagitov [7] and usually referred to as the Λcoalescents. These are Markov proc ..."
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The Bolthausen–Sznitman coalescent was introduced in the context of spin glasses in [1]. These days, it is usually thought of as a special case of a more general class of coalescent processes introduced by Pitman [5] and Sagitov [7] and usually referred to as the Λcoalescents. These are Markov
On asympotics of the betacoalescents
 arXiv:1203.3110, 2012. 20 ROMAIN ABRAHAM AND JEANFRANÇOIS
"... We show that the total number of collisions in the exchangeable coalescent process driven by the beta (1, b) measure converges in distribution to a 1stable law, as the initial number of particles goes to infinity. The stable limit law is also shown for the total branch length of the coalescent tree ..."
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Cited by 4 (1 self)
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tree. These results were known previously for the instance b = 1, which corresponds to the Bolthausen–Sznitman coalescent. The approach we take is based on estimating the quality of a renewal approximation to the coalescent in terms of a suitable Wasserstein distance. Application of the method to beta
Results 1  10
of
230