On random trees

By Tamás F. Móri. 2002

533 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/06d1cb35d032812106d3c2f5edd4d06e524c682e

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

On a preferential attachment and generalized Pólya’s urn model (2012, background): “In [4] and [19], respectively, in [25], the authors give the limiting degree distribution for a wide range of linear, respectively, sub-linear, weight functions.”
The Genealogy of Self-similar Fragmentations with Negative Index as a Continuum Random Tree (2004, unknown): “Yet, we point out that when S s − 1 1 − 1 ν (d s ) = ∞ , one anyway obtains the following bounds for the Hausdorﬀ dimension of L ( T F ): where It is worth noting that these results allow as a special case to compute the Hausdorﬀ dimen-sion of the so-called stable trees of Duquesne and Le Gall [14],”
A continuum-tree-valued Markov process (2009, methodology): “To better understand the links between the Lévy CRT and the exploration process, we can combine the Markov property with the other Poisson decomposition of [17], Lemma 4.”
Invariance principles for Galton-Watson trees conditioned on the number of leaves (2011, background): “The notion of the height process was introduced in [24] and studied in great detail in [12]; see Section 5.”
Sub-Gaussian tail bounds for the width and height of conditioned Galton--Watson trees (2010, unknown): “[1], [5], [10] and [9]; moreover, they converge jointly [5], [16], ( n−1/2W (Tn), nH(Tn) ) d −→ (σW, σ−1H) (1.”
Random Graph Dynamics: References (2006, background): “Mori’s martingales. Mori (2004) has studied the case 4 model from the previous section.”
Limit laws for functions of fringe trees for binary search trees and random recursive trees (2015, methodology): “In this paper we consider fringe trees of the random binary search tree as well as of the random recursive tree; recall that a fringe tree is a subtree consisting of some node and all its descendants, see Aldous [1] for a general theory, and note that fringe trees typically are ”small” compared to…”
The continuum limit of critical random graphs (2009, background): “4 of Duquesne and Le Gall [18] for a proof).”
Stochastic flows associated to coalescent processes. III. Limit theorems (2005, background): “, [9]) allows one to interpret each of these atoms as the size of a family of individuals at time t that have the same ancestor at the initial time.”
Growth of preferential attachment random graphs via continuous-time branching processes (2007, methodology): “We remark this basic model creates a growing “tree” with undirected edges, and includes the “one-edge” case of the original Barabasi-Albert process, made precise in [8], by setting Xi ≡ 1 and β = 0, as well as the “β ≥ 0” scheme considered in [13] and [14], by taking Xi ≡ 1.”
Random Graphs and Complex Networks (2016, background): “2 are novel, but the combinatorial arguments are following Eckhoff et al. (2013), where shortest weighted paths in the complete graph are investigated.”
A new family of Markov branching trees: the alpha-gamma model (2008, background): “They also contain growth rules for a model [18, 20] based on the stable tree of Duquesne and Le Gall [7], for the cases γ = 1 − α , 1 / 2 ≤ α < 1, where all edges are given the same weight; we show here that these cases γ = 1 − α , 1 / 2 ≤ α ≤ 1, as well as α = γ = 0 form the intersection with the e”
Recent progress in coalescent theory (2009, unknown): “Bertoin and Le Gall [29], in their first joint paper on coalescence, showed that the Bolthausen-Sznitman coalescent process was embedded in the genealogy of a certain continuous-state branching process (CSBP), which is the CSBP associated with the branching mechanism ψ(u) = u log u, u ≥ 0.”
An almost-bijective proof of an asymptotic property of partitions (2007, background): “In [4] and [11] the authors derive the asymptotic degree distribution for a model that is equivalent to the special case, when the weight function is linear.”
Fringe trees, Crump-Mode-Jagers branching processes and $m$-ary search trees (2016, methodology): “The model with general wk was considered by Móri [102].”
Random stable looptrees (2013, unknown): “We refer to [13] and [14] for details and proofs of the assertions contained in this section.”
Simply generated trees, conditioned Galton–Watson trees, random allocations and condensation (2011, background): “(See e.g. Drmota [10] for several such results of different types.)”