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A continuumtreevalued Markov process
"... Abstract. We present a construction of a Lévy continuum random tree (CRT) associated with a supercritical continuous state branching process using the socalled exploration process and a Girsanov’s theorem. We also extend the pruning procedure to this supercritical case. Let ψ be a critical branchi ..."
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Cited by 22 (12 self)
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Abstract. We present a construction of a Lévy continuum random tree (CRT) associated with a supercritical continuous state branching process using the socalled exploration process and a Girsanov’s theorem. We also extend the pruning procedure to this supercritical case. Let ψ be a critical
Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models
 Ann. Probab
, 2008
"... Given any regularly varying dislocation measure, we identify a natural selfsimilar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of Aldous’s betasplitting models and Ford’s alpha models for phyl ..."
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Cited by 37 (13 self)
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Given any regularly varying dislocation measure, we identify a natural selfsimilar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of Aldous’s betasplitting models and Ford’s alpha models
The continuum random tree. II. An overview
 In Stochastic Analysis
, 1990
"... Many different models of random trees have arisen in a variety of applied setting, and there is a large but scattered literature on exact and asymptotic results for particular models. For several years I have been interested in what kinds of "general theory " (as opposed to ad hoc analysis ..."
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Cited by 103 (13 self)
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Many different models of random trees have arisen in a variety of applied setting, and there is a large but scattered literature on exact and asymptotic results for particular models. For several years I have been interested in what kinds of "general theory " (as opposed to ad hoc
CONTINUUM
"... In this thesis I will demonstrate that there is a similarity between the use of physical walls and digital walls as means of ideological dissemination by power structures as well as sociopolitical protesters. Also, I will show that their use in this manner not only changes the way that both functio ..."
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In this thesis I will demonstrate that there is a similarity between the use of physical walls and digital walls as means of ideological dissemination by power structures as well as sociopolitical protesters. Also, I will show that their use in this manner not only changes the way that both function ideologically, but also changes the environment that these walls are created/exist in as well. The first case study will analyze Banksy’s employment of carnivalesque graffiti as a means of protest. The second case study will analyze the use of digital public space and “walls ” created within social media as tools of protest, paralleling the earlier examples pertaining to the physical walls of public space. The third case study will look at the employment of the digital “walls ” of Facebook and Twitter in conjunction with the use of public space in Cairo and its role in the
Deterministic and Stochastic Models for Coalescence (Aggregation, Coagulation): a Review of the MeanField Theory for Probabilists
 Bernoulli
, 1997
"... Consider N particles, which merge into clusters according to the rule: a cluster of size x and a cluster of size y merge at (stochastic) rate K(x; y)=N , where K is a specified rate kernel. This MarcusLushnikov model of stochastic coalescence, and the underlying deterministic approximation given by ..."
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Cited by 222 (13 self)
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are only now starting to be studied rigorously, so many interesting open problems appear. Keywords. branching process, coalescence, continuum tree, densitydependent Markov process, gelation, random graph, random tree, Smoluchowski coagulation equation Research supported by N.S.F. Grant DMS9622859 1
Treegraded spaces and asymptotic cones of groups
, 2005
"... We introduce a concept of treegraded metric space and we use it to show quasiisometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic cones, to find geometric properties of Cayley graphs of rel ..."
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Cited by 141 (15 self)
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We introduce a concept of treegraded metric space and we use it to show quasiisometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic cones, to find geometric properties of Cayley graphs
Reversing the cut tree of the Brownian continuum random tree
, 2014
"... Consider the logging process of the Brownian continuum random tree (CRT) T using a Poisson point process of cuts on its skeleton [Aldous and Pitman, Ann. Probab., vol. 26, pp. 1703–1726, 1998]. Then, the cut tree introduced by Bertoin and Miermont describes the genealogy of the fragmentation of T i ..."
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Consider the logging process of the Brownian continuum random tree (CRT) T using a Poisson point process of cuts on its skeleton [Aldous and Pitman, Ann. Probab., vol. 26, pp. 1703–1726, 1998]. Then, the cut tree introduced by Bertoin and Miermont describes the genealogy of the frag
Regenerative tree growth: binary selfsimilar continuum random trees and PoissonDirichlet compositions
, 2009
"... We use a natural ordered extension of the Chinese Restaurant Process to grow a twoparameter family of binary selfsimilar continuum fragmentation trees. We provide an explicit embedding of Ford’s sequence of alpha model trees in the continuum tree which we identified in a previous article as a dist ..."
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Cited by 16 (6 self)
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We use a natural ordered extension of the Chinese Restaurant Process to grow a twoparameter family of binary selfsimilar continuum fragmentation trees. We provide an explicit embedding of Ford’s sequence of alpha model trees in the continuum tree which we identified in a previous article as a
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