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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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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
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Rooted trees and moments of large sparse random matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 In these expository paper we describe the role of the rooted trees as a base for convenient tools in studies ofrandom matrices. Regarding the Wigner ensemble of random matrices, we represent main ingredients ofthis approach.
Oleksiy Khorunzhiy
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The spectral dimension of random trees [PDF]
Journal of Physics A: Mathematical and General, 2002 We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new scaling hypothesis for the Gaussian model on generic bounded graphs and in favor of a previously conjectured exact ...
C. Destri, Luca Donetti
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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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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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Additive tree functionals with small toll functions and subtrees of random trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Many parameters of trees are additive in the sense that they can be computed recursively from the sum of the branches plus a certain toll function. For instance, such parameters occur very frequently in the analysis of divide-and-conquer algorithms. Here
Stephan Wagner
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On the spectral dimension of random trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 We determine the spectral dimensions of a variety of ensembles of infinite trees. Common to the ensembles considered is that sample trees have a distinguished infinite spine at whose vertices branches can be attached according to some probability ...
Bergfinnur Durhuus +2 more
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Random Trees in Random Graphs [PDF]
Proceedings of the American Mathematical Society, 1988 We show that a random labeled n n -vertex graph almost surely contains isomorphic copies of almost all labeled n n -vertex trees, in two senses. In the first sense, the probability of each edge occurring in the graph diminishes as n n increases, and the set of trees referred to as "almost all" depends
Nicholas C. Wormald, Edward A. Bender
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A functional limit law for the profile of plane-oriented recursive trees. [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We give a functional limit law for the normalized profile of random plane-oriented recursive trees. The proof uses martingale convergence theorems in discrete and continuous-time. This complements results of Hwang (2007).
Henning Sulzbach
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