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Fragmentation of Random Trees [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected existing node.
Ben-Naim, E., Kalay, Z.
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Random ultrametric trees and applications [PDF]
ESAIM: Proceedings and Surveys, 2017 Ultrametric trees are trees whose leaves lie at the same distance from the root. They are used to model the genealogy of a population of particles co-existing at the same point in time.
Lambert, Amaury
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Ergodic Theory and Dynamical Systems, 2012 We consider unimodular random rooted trees (URTs) and invariant forests in Cayley graphs. We show that URTs of bounded degree are the same as the law of the component of the root in an invariant percolation on a regular tree.
Aldous +5 more
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Acta Mathematica Hungarica, 2014 Local convergence of bounded degree graphs was introduced by Benjamini and Schramm. This result was extended further by Lyons to bounded average degree graphs.
Deák, Attila
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Width and mode of the profile for some random trees of logarithmic height
Annals of Applied Probability, 2006 We propose a new, direct, correlation-free approach based on central moments of profiles to the asymptotics of width (size of the most abundant level) in some random trees of logarithmic height.
Luc Devroye, Hsien-Kuei Hwang
exaly +3 more sources
Profiles of random trees: plane-oriented recursive trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We summarize several limit results for the profile of random plane-oriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximations of the expected width and the ...
Hsien-Kuei Hwang
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On random trees and forests [PDF]
ESAIM: Proceedings and Surveys, 2023 The first talk at the session Random trees and random forests “Journée MAS” (27/08/2021) was presented by I. Kortchemski. After a general up-to-date introduction to local and scaling limits of Bienaymé trees (which are discrete branching trees), he ...
Contat Alice +4 more
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Conditioned Galton-Watson trees do not grow [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 An example is given which shows that, in general, conditioned Galton-Watson trees cannot be obtained by adding vertices one by one, while this can be done in some important but special cases, as shown by Luczak and Winkler.
Svante Janson
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Extremely randomized trees [PDF]
Machine Learning, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Geurts, Pierre +2 more
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Random Records and Cuttings in Split Trees: Extended Abstract [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We study the number of records in random split trees on $n$ randomly labelled vertices. Equivalently the number of random cuttings required to eliminate an arbitrary random split tree can be studied.
Cecilia Holmgren
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