Results 11 to 20 of about 723,488 (236)
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. As nodes are removed from the tree, one at a time, the tree dissolves into an ensemble of separate trees,
Kalay, Z, Ben-Naim, E
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Ergodic Theory and Dynamical Systems, 2013 AbstractWe 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. We use this to give a new proof that URTs are sofic, a result of Elek.
Oded Schramm +2 more
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Acta Mathematica Hungarica, 2013 Local convergence of bounded degree graphs was introduced by Benjamini and Schramm. This result was extended further by Lyons to bounded average degree graphs. In this paper, we study the convergence of a random tree sequence where the probability of a given tree is proportional to $\prod_{v_i\in V(T)}d(v_i)!$.
Deák, Attila
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Journal of Statistical Mechanics: Theory and Experiment, 2010 We investigate a network growth model in which the genealogy controls the evolution. In this model, a new node selects a random target node and links either to this target node, or to its parent, or to its grandparent, etc; all nodes from the target node to its most ancient ancestor are equiprobable destinations.
Paul L. Krapivsky, Eli Ben-Naim
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Annales de la Faculté des sciences de Toulouse : Mathématiques, 2009 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
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Random environment on coloured trees [PDF]
Bernoulli, 2007 In this paper, we study a regular rooted coloured tree with random labels assigned to its edges, where the distribution of the label assigned to an edge depends on the colours of its endpoints. We obtain some new results relevant to this model and also show how our model generalizes many other probabilistic models, including random walk in random ...
Menshikov, Mikhail +2 more
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Multicritical continuous random trees
Journal of Statistical Mechanics: Theory and Experiment, 2006 We introduce generalizations of Aldous' Brownian Continuous Random Tree as scaling limits for multicritical models of discrete trees. These discrete models involve trees with fine-tuned vertex-dependent weights ensuring a k-th root singularity in their generating function. The scaling limit involves continuous trees with branching points of order up to
Bouttier, Jérémie +2 more
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Spreading of Infections on Network Models: Percolation Clusters and Random Trees
Mathematics, 2021 We discuss network models as a general and suitable framework for describing the spreading of an infectious disease within a population. We discuss two types of finite random structures as building blocks of the network, one based on percolation concepts
Hector Eduardo Roman, Fabrizio Croccolo
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One-sided Variations on Tries: Path Imbalance, Climbing, and Key Sampling [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 One-sided variations on path length in a trie (a sort of digital trees) are investigated: They include imbalance factors, climbing under different strategies, and key sampling.
Costas A. Christophi, Hosam M. Mahmoud
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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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