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Annales Fac. Sci. Toulouse Ser. 6, Vol. XV, pp. 35-62, 2006, 2006 We survey recent developments about random real trees, whose prototype is the Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees.
Gall, J. F. Le
arxiv +7 more sources
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
doaj +5 more sources
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
core +8 more sources
Optimal Prefetching in Random Trees [PDF]
Mathematics, 2021 We propose and analyze a model for optimizing the prefetching of documents, in the situation where the connection between documents is discovered progressively.
Kausthub Keshava +2 more
doaj +6 more sources
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
core +5 more sources
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.
core +6 more sources
Fringe trees, Crump-Mode-Jagers branching processes and $m$-ary search trees [PDF]
arXiv, 2016 This survey studies asymptotics of random fringe trees and extended fringe trees in random trees that can be constructed as family trees of a Crump-Mode-Jagers branching process, stopped at a suitable time. This includes random recursive trees, preferential attachment trees, fragmentation trees, binary search trees and (more generally) $m$-ary search ...
Holmgren, Cecilia, Janson, Svante
arxiv +3 more sources
Tree limits and limits of random trees [PDF]
Combinatorics, Probability and Computing, 2020 We explore the tree limits recently defined by Elek and Tardos. In particular, we find tree limits for many classes of random trees. We give general theorems for three classes of conditional Galton-Watson trees and simply generated trees, for split trees and generalized split trees (as defined here), and for trees defined by a continuous-time branching
arxiv +7 more sources
arXiv, 2014 We prove that a random labeled (unlabeled) tree is balanced. We also prove that random labeled and unlabeled trees are strongly $k$-balanced for any $k\geq 3$.
Warren E. Shreve, Azer Akhmedov
arxiv +5 more sources
Random walks on random trees [PDF]
Journal of the Australian Mathematical Society, 1973 Let T denote one of the nn−2 trees with n labelled nodes that is rooted at a given node x (see [6] or [8] as a general reference on trees). If i and j are any two nodes of T, we write i ∼ j if they are joined by an edge in T. We want to consider random walks on T; we assume that when we are at a node i of degree d the probability that we proceed to ...
J. W. Moon
openalex +3 more sources