Homogeneous fragmentation processes

By Jean Bertoin. 2001

143 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e7d8bb731c37109035a8ff12c5b92eb8208cc409

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In Applied Mathematics

In Computational Mechanics

In Mathematical Physics

Citations in the corpus

A new family of Markov branching trees: the alpha-gamma model (2008, background): “…for it is For general ( α, γ ), the explicit form of the dislocation measure in size-biased order, specifically the density g α,γ of the ﬁrst marginal of ν sb α,γ , yields immediately the tagged particle [4] L´evy measure associated with a fragmentation process with alpha-gamma dislocation measure.”
Combinatorial Stochastic Processes (2006, methodology): “For instance there is a representation of both coagulation and fragmentation semigroups, analogous to a Lévy-Khintchine representation, as has been shown by Schweinsberg [396] and Bertoin [45].”
Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models (2006, methodology): “As first discussed in Bertoin [8], a convenient way to study homogeneous fragmentation processes is to use a “discretization of space.””
The Genealogy of Self-similar Fragmentations with Negative Index as a Continuum Random Tree (2004, unknown): “It is done following [6, 7] by a Poissonian construction.”
Discretization Methods for Homogeneous Fragmentations (2004, background): “According to Theorem 2 in [4], there exists a unique measure μ on P which is exchangeable (i.”
Self-similar fragmentations derived from the stable tree I (2003, methodology): “Proof. Suppose β = 0, then the result is almost immediate by the results of [ 8 ] on homogeneous fragmentation processes.”
Gibbs fragmentation trees (2007, methodology): “The integral representation (5) stems from an association with Bertoin’s theory of homogeneous fragmentation processes in continuous-time [4].”
Self-similar fragmentations (2002, methodology): “We conclude this section by noting that the following construction of a self-similar P-valued fragmentation/ with characteristics(α, c, ν) is implicit in Theorem 3: one first constructs a homogeneous P-valued fragmentatioñ/ with erosion ratec and Lévy measureν as in [6], and then one takes /= /̃.”
Multifractal spectra and precise rates of decay in homogeneous fragmentations (2006, background): “For U = ( a 1 , b 1 ) ∈ U , we deﬁne the aﬃne transformation g U : (0 , 1) → U given by g U ( x ) = a 1 + x ( b 1 − a 1 ).”
Exchangeable Fragmentation-Coalescence Processes and their Equilibrium Measures (2004, methodology): “See [4] for the demonstration concerning F .”
The asymptotic behavior of fragmentation processes (2003, methodology): “In [6,7], we considered a class of Markov processes X = (X(t), t ≥ 0) with values in S↓, called self-similar fragmentations, which fulfill both the so-called fragmentation and the scaling properties.”
Poisson Process Partition Calculus with applications to Exchangeable models and Bayesian Nonparametrics (2002, methodology): “Kingman’ s result is based on a modification of Blackwell’s (1973) argument for the Dirichlet process.”
Limit theorems for Markov processes indexed by continuous time Galton--Watson trees (2009, background): “rete-time Galton–Watson processes. Other motivating topics for this kind of results come from branching random walks (see, e.g., Biggins [13], Rouault [51]) and homogeneous fragmentation (see Bertoin [10, 11]). We refer to the examples in Section 5 for more details. The law of large numbers that we ”
Ranked Fragmentations (2006, methodology): “In [5] Bertoin showed that the semi-group of a homogeneous partition fragmentation (the definition and main properties of partition fragmentations are discussed in Sect.”
Self-similar fragmentations derived from the stable tree II: splitting at nodes (2004, background): “Such fragmentations have been introduced and extensively studied by Bertoin in [8, 9].”
Spinal partitions and invariance under re-rooting of continuum random trees (2007, unknown): “We refer to Bertoin’s book [10] and the above mentioned papers [8, 9] for details on these time-changes and background on homogeneous and self-similar fragmentations.”
Critical Gaussian multiplicative chaos: Convergence of the derivative martingale (2012, background): “[25] HELFFER, B. and NIER, F. (2006). Quantitative analysis of metastability in reversible diffusion”
Martingales and Profile of Binary Search Trees (2004, unknown): “As a consequence of the general theory of homogeneous fragmentations (see Bertoin [7]) or by a direct computation, we see that (s(t), t ≥ 0) is an homogeneous Poisson process with parameter 1.”