Random Trees: An Interplay between Combinatorics and Probability

By M. Drmota. 2009

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Branching random walks (2015, background): “The resulting tree is a planted tree (in the sense of [100]).”
Sub-Gaussian tail bounds for the width and height of conditioned Galton--Watson trees (2010, background): “More precisely, n−1/2W(Tn) and n−1/2H(Tn) both converge in distribution, as n → ∞; see, for example, [1, 5, 11] and [10]; moreover, they converge jointly [5, 20], ( n−1/2W(Tn), n−1/2H(Tn) ) d −→ (σW,σ−1H ) (3)”
Scaling limits of Markov branching trees with applications to Galton–Watson and random unordered trees (2010, methodology): “ plane trees will be called (rooted) unordered trees, or simply trees as opposed to plane trees, and denoted by lowercase letter t’s. They are sometimes called (rooted) Po´lya trees in the literature [16]. Given a tree t, we will freely adapt some notation from plane trees when dealing with quantiti”