The Bolthausen–Sznitman coalescent and the genealogy of continuous-state branching processes

By Jean Bertoin, Jean-François Le Gall. 2000

164 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1ba3843b94edab5d3dc5ef316b229c8bea4b8558

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Stochastic flows associated to coalescent processes. III. Limit theorems (2005, unknown): “Such connections were already derived in [ 3 ], where the Bolthausen-Sznitman coalescent was shown to describe the genealogical structure of a particular continuous-state branching process introduced by Neveu, and in [6], where similar relations were obtained between the so-called beta-coalescents a”
Coalescence times for the branching process (2003, background): “It is known that, under our assumptions, ut (·) is the Lévy exponent of a subordinator S, which has finite Lévy measure 't and drift coefficient zero (see [3]), so that”
Alpha-Stable Branching and Beta-Coalescents (2005, background): “Also, � is the uniform distribution on [0,1], so the �-coalescent is the Bolthausen-Sznitman coalescent, which was introduced in [5], so this case corresponds to the result of Bertoin and Le Gall [ 2 ].”
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”
Combinatorial Stochastic Processes (2006, background): “See [322, 72, 50, 54, 357] for further developments of the low temperature case, related to continuous state branching processes, Ruelle’s probability cascades, and the Bolthausen-Sznitman coalescent.”
Stochastic Models for Structured Populations: Scaling Limits and Long Time Behavior (2015, background): “An other point of view, using the flow of subordinators which comes by letting the initial size vary, has been exhibited recently by Bertoin and Le Gall [12].”
Small-time behavior of beta coalescents (2006, unknown): “The α = 1 case had previously been established by Bertoin and Le Gall [6].”
The coalescent structure of continuous-time Galton–Watson trees (2017, background): “It also makes appearences in the coalescent structure of Neveu’s CSBP [9] and of branching Brownian motion on the half-line [7].”
Random Recursive Trees and the Bolthausen-Sznitman Coalesent (2005, methodology): “ collisions (also 1 known as Λ-coalescents), gave a construction of them based on Poisson random measures and studied the Bolthausen-Sznitman coalescent as a member of this class. Bertoin and Le Gall [4] give an alternative derivation in terms of the genealogy of a continuous-state branching process”
On the extinction of Continuous State Branching Processes with catastrophes (2013, unknown): “= 1+ Md(q)(e(˚+K (1)+j j)=q 1) c 3(q) : We then prove that lim q!1c 3(q) is positive using similar arguments as previously. 4.4 Proof of Theorem 7 Proof of Theorem 7 a/ (i). Recall from Lemma II.2 in [6] that the process (K t K (t s) ;0 st) has the same law as (K s;0 st). Then Z t 0 e K sds= Z t 0 e”