Stochastic flows associated to coalescent processes

By Jean Bertoin, Jean-François Le Gall. 2003

213 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/ebdd4c06a4cbc60c2aaa4930e5bed2e933f3fe2f

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Citations in the corpus

Proof(s) of the Lamperti representation of Continuous-State Branching Processes (2008, background): “Similar integral equations appear in [4] and [8].”
Recent progress in coalescent theory (2009, unknown): “The generalisation which was considered by Bertoin and Le Gall in [30] for Λ-coalescents was the following.”
Population Dynamics and Random Genealogies (2008, background): “One of the tasks of Ref.[13] was to construct a flow of bridges in continuous time.”
Stochastic flows associated to coalescent processes. III. Limit theorems (2005, methodology): “Then, for each fixed t ≥ 0, Jt and Dt have the same distribution (Theorem 1 in [ 4 ] indeed gives a deeper connection, which has been briefly described in Section 1).”
Small-time behavior of beta coalescents (2006, unknown): “1 of [11] states that the process (MR−1(t)/Z(R (t)), t ≥ 0) has the same law as the Λ-Fleming– Viot process introduced in [7], where Λ is the Beta(2−α,α) distribution.”
The Λ-coalescent speed of coming down from infinity (2008, background): “The speed of CDI was recently determined for Beta-coalescents and their “perturbations” in Berestycki, Berestycki and Schweinsberg [4] and [5] and Bertoin and Le Gall [6] (where convergence is established in probability).”
Alpha-Stable Branching and Beta-Coalescents (2005, methodology): “Thus, R is precisely of the form appearing in [ 3 ] p. 280, and the second summand on the right hand side of (3.10) is const ·z1 �(RG)(�).”
A coalescent model for the effect of advantageous mutations on the genealogy of a population (2004, background): “Coalescents with simultaneous multiple collisions, which were studied byMo ¨ hle and Sagitov [20], Schweinsberg [28], and Bertoin and LeGall [ 4 ], have the propertythat manyblocks”
BETA-COALESCENTS AND CONTINUOUS STABLE RANDOM TREES (2006, background): “If we ask for finer limit theorems about the genealogy of (Zt, t≥ 0), then Duquesne and Le Gall have shown that the discrete height process (Hnk , k = 0,1, . . .), where Hnk is the generation of the kth individual, converges when suitably normalized to a process (Ht, t ≥ 0) called the height process”
Lamperti-type laws (2007, methodology): “However, the intensity νt, which plays a fundamental role in (6; 9) is only known up to its Laplace transform.”
Combinatorial Stochastic Processes (2006, background): “Bertoin and Le Gall [51] show that the correspondence between operations of coagulation and subordination, described by Lemma 5.”