Convergence of Discrete Snakes

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Invariance principles for spatial multitype Galton–Watson trees (2006, background): “By contrast with [10] and [13], our hypothesis on the spatial displacement is an (8+ ξ )-moment assumption rather than a (4 + ξ )-moment assumption.”
The topological structure of scaling limits of large planar maps (2006, background): “1 in [22], which is itself a conditional version of invariance principles relating discrete snakes to the Brownian snake [18].”
Conditioned Brownian trees (2005, unknown): “Theorem 1.2 Let s∗ be the unique time of the minimum of Ŵ on [0, 1].”
Scaling limits of random planar maps with a unique large face (2012, background): “See, for example, [31], and thus Ŝn n (t) is typically of the order n−1/4.”
THE DENSITY OF THE ISE AND LOCAL LIMIT LAWS FOR EMBEDDED TREES (2005, unknown): “1) holds, with γ := σ−1 η σ 1/2 ξ [4]; see also [17].”
Random real trees (2006, background): “A recent paper of Marckert and Mokkadem [52] uses ideas related to the previous discussion to construct the Brownian map, which is a candidate for the continuous limit of random quadrangulations.”
Limit of normalized quadrangulations: The Brownian map (2004, background): “(60) is false (see analogous considerations for the limit of discrete snake in Janson & Marckert [ 23 ]).”
Scaling limits of random trees and planar maps (2011, background): “More general results can be found in [25].”