An invariance principle for random planar maps

By Grégory Miermont. 2006

50 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d47c701eb035b8173f9adc96ae0cdb5524964892

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Citations in the corpus

Scaling limits of random trees and planar maps (2011, methodology): “A recent work of Haas and Miermont [23] provides further extensions of Theorem 3.9 to Pólya trees (unordered rooted trees).”
Invariance principles for spatial multitype Galton–Watson trees (2006, background): “Applications of these results to random planar maps are discussed in the companion paper [14].”
Scaling limits of random planar maps with large faces (2011, result): “Assuming certain integrability conditions on the sequence of weights, Marckert and Miermont [21] obtain a variety of limit theorems for large random bipartite planar maps chosen according to these Boltzmann distributions.”
Uniqueness and universality of the Brownian map (2011, methodology): “The results of Chassaing and Schaeffer were extended to more general classes of random maps in several papers of Miermont and his co-authors (see in particular [20, 23]), using the bijections with trees found in [4].”
The Brownian map is the scaling limit of uniform random plane quadrangulations (2011, background): “ the question of universality. It is expected that Theorem1remains valid for much more general families of random maps than quadrangulations, namely, the regular critical Boltzmann maps introduced in [20,22] should admit the Brownian map as a scaling limit. In particular, in his work mentioned at th”
Some families of increasing planar maps (2007, background): “Then, – Marckert & Mokkadem [37] showed the same result for pointed quadrangulations with n faces, – Marckert & Miermont [35] showed that up to a normalizing constant, the same asymptotic holds for pointed rooted bipartite maps under Boltzmann distribution with n faces, (the weight of a bipartite ma”
Geodesics in large planar maps and in the Brownian map (2008, background): “In a recent paper [30], Miermont has obtained, independently of the present work, certain uniqueness results for geodesics in continuous limits of discrete quadrangulations, in a setting which is however different from ours.”