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Discrete Applied Mathematics, 2019 Let $T$ be a random tree taken uniformly at random from the family of labelled trees on $n$ vertices. In this note, we provide bounds for $c(n)$, the number of sub-trees of $T$ that hold asymptotically almost surely. With computer support we show that $1.41805386^n \le c(n) \le 1.41959881^n$. Moreover, there is a strong indication that, in fact, $c(n) \
Bogumił Kamiński, Paweł Prałat
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Concentration Properties of Extremal Parameters in Random Discrete Structures [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 The purpose of this survey is to present recent results concerning concentration properties of extremal parameters of random discrete structures. A main emphasis is placed on the height and maximum degree of several kinds of random trees. We also provide
Michael Drmota
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Gordon-Scantlebury and Platt Indices of Random Plane-oriented Recursive Trees [PDF]
Mathematics Interdisciplinary Research, 2021 For a simple graph G, the Gordon-Scantlebury index of G is equal to the number of paths of length two in G, and the Platt index is equal to the total sum of the degrees of all edges in G.
Ramin Kazemi
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Perturbative Quantum Field Theory on Random Trees [PDF]
Communications in Mathematical Physics, 2019 In this paper we start a systematic study of quantum field theory on random trees. Using precise probability estimates on their Galton–Watson branches and a multiscale analysis, we establish the general power counting of averaged Feynman amplitudes and ...
N. Delporte, V. Rivasseau
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ESAIM: Proceedings, 2011 These notes provide an elementary and self-contained introduction to branching ran- dom walks. Section 1 gives a brief overview of Galton-Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly in- dispensable, but they introduce the idea of using size-biased trees,
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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. 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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The height of random binary unlabelled trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a central and local
Nicolas Broutin, Philippe Flajolet
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Recursive construction of continuum random trees [PDF]
Annals of Probability, 2016 We introduce a general recursive method to construct continuum random trees (CRTs) from independent copies of a random string of beads, that is, any random interval equipped with a random discrete probability measure, and from related structures.
Franz Rembart, Matthias Winkel
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Election algorithms with random delays in trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 The election is a classical problem in distributed algorithmic. It aims to design and to analyze a distributed algorithm choosing a node in a graph, here, in a tree. In this paper, a class of randomized algorithms for the election is studied.
Jean-François Marckert +2 more
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On the number of transversals in random trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We study transversals in random trees with n vertices asymptotically as n tends to infinity. Our investigation treats the average number of transversals of fixed size, the size of a random transversal as well as the probability that a random subset of ...
Bernhard Gittenberger, Veronika Kraus
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