Itô’s excursion theory and random trees

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Invariance principles for Galton-Watson trees conditioned on the number of leaves (2011, background): “In a different but related direction, the effect of conditioning a GaltonWatson tree on having height equal to n has been studied [16, 18, 22], and Broutin & Marckert [6] have investigated the asymptotic behavior of uniformly distributed trees with prescribed degree sequence.”
A Simple Proof of Duquesne’s Theorem on Contour Processes of Conditioned Galton–Watson Trees (2011, methodology): “This has been proved by Le Gall in [17] when μ has finite variance.”
Scaling Limits of Random Graphs from Subcritical Classes (2014, background): “2 implies convergence with respect to the Gromov–Hausdorff metric; see [36], page 740.”
Scaling limits of Markov branching trees and Galton-Watson trees conditioned on the number of vertices with out-degree in a given set (2011, methodology): “The Otter–Dwass formula (see [11]) has been an essential tool in several proofs that the Brownian continuum random tree is the scaling limit of Galton–Watson trees conditioned on their number of vertices, including the original proof in [2] as well as newer proofs in [9] and [5].”
Rescaled bipartite planar maps converge to the Brownian map (2013, methodology): “The fact that we are here conditioning on the total number of vertices creates a significant additional difficulty, which we handle through an absolute continuity argument similar to the ones used in Section 6 of [10].”