Random fragmentation and coagulation processes

By Jean Bertoin. 2006

558 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3912e6c98c667da37e5e708a1dbcf6b09f5a14ff

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In Water Science and Technology

Citations in the corpus

Population Dynamics and Random Genealogies (2008, background): “Without even speaking of tools from the “omics” era, there are at least two examples of recent, active fields of probability theory related to population biology: genealogy, or phylogeny, modelling and reconstruction[11,35], whose toy model is the Kingman coalescent[74], and social networks[34], who”
Fringe trees, Crump-Mode-Jagers branching processes and $m$-ary search trees (2016, background): “(The related intrinsic martingale in [9] is constant 1 too, see [9, Section 1.”
Limit distributions for large P\'{o}lya urns (2009, background): “For a very synthetic reference on semi-groups of Markov continuous-time processes, one can refer to Bertoin [3], Chapter 1.”
Statistical estimation of a growth-fragmentation model observed on a genealogical tree (2012, methodology): “By fragmentation techniques inspired by Bertoin [7], see also Haas [21], we relate the process ( X, V ) to a growth-fragmentation equation as follows.”
Fluctuations of Lévy Processes with Applications (2014, methodology): “This was provided by Chung and Fuchs (1951) and Erickson (1973) for random walks; see also Bertoin (1997). To state their criteria, recall with the help of Theorem 3.”
Branching random walks (2015, background): “If t > 0 is such that ψ(t) = 0, the value of t is often referred to as a “Malthusian parameter” in various contexts (Jagers [147], Nerman [202], Bertoin [47], etc.”
Recent progress in coalescent theory (2009, unknown): “obtain immediately (27). Coalescent theory 41 It is possible to prove (27) directly on Kingman’s coalescent by induction, which is the one chosen by Kingman [107] (see also Proposition 2.1 of Bertoin [28]). However this approach requires to guess the formula beforehand, which is really not that obvi”
Novel scaling limits for critical inhomogeneous random graphs (2009, background): “r λ. It shall not be possible to give a full description of the process and its many fascinating properties here and we refer the interested reader to the paper [3], the survey paper [2] and the book [5]. Write l2 ↓ to be the metric space of inﬁnite real-valued sequences x = (x1,x2 ...) with x1 ≥ x2”