Scaling limits of random planar maps with large faces

By Jean-François Le Gall, Grégory Miermont. 2011

135 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/caf622caf1f83af2db29f676cf2833137fe4f3d8

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Scaling limits of random trees and planar maps (2011, background): “One may ask what happens for random planar maps such that the distribution of the degree of a typical face has a heavy tail: This problem is discussed in [33], where it is shown that this case leads to different scaling limits.”
The Brownian map is the scaling limit of uniform random plane quadrangulations (2011, background): “A one-parameter family of scaling limits of maps, different from the Brownian map, can be obtained by considering Boltzmann distributions on maps for which the degrees of faces have heavy tails [18].”
Random stable looptrees (2013, unknown): “We refer to [17] and [18] for details and proofs of the assertions contained in this section.”
Conformal loop ensembles: the Markovian characterization and the loop-soup construction (2010, background): “It is possible that the CLEs are related to random planar maps chosen in such a way that they contain “large holes,” as described in [21].”
Scaling Limits for Random Quadrangulations of Positive Genus (2010, methodology): “These results may be seen as a conditioned version of some of Miermont’s results appearing in [23].”
Scaling Limit of Random Planar Quadrangulations with a Boundary (2011, methodology): “As we consider in this work surfaces with a boundary, the notion of 1-regularity used by Miermont in [Mie08] is no longer sufficient: we will also need here the notion of 0-regularity, which we will expose in Section 5.1.”
Sub-exponential tail bounds for conditioned stable Bienaymé–Galton–Watson trees (2015, background): “Bienaymé–Galton–Watson trees belonging to domains of attraction of stable laws have recently appeared in a number of two-dimensional statistical physics models, in connection with scaling limits of random maps with large faces [34], scaling limits of critical site-percolation clusters on infinite ra”
A Simple Proof of Duquesne’s Theorem on Contour Processes of Conditioned Galton–Watson Trees (2011, unknown): “In this work, we give an alternative proof of Duquesne’s result, which is based on an idea that appeared in the recent papers [17, 19].”
Random geometry on the sphere (2014, background): “One indeed expects that the Brownian map will appear as the scaling limit of very general random planar maps provided some bound holds on the distribution of the degree of a typical face (on the other hand, the paper [33] shows that different scaling limits may occur if one considers distributions t”
Scaling limits of random planar maps with a unique large face (2012, methodology): “Furthermore, the distributions are closely related to distributions arising in certain statistical mechanical models on random maps as is discussed in [41].”
Invariance principles for Galton-Watson trees conditioned on the number of leaves (2011, background): “ A(˝) = n] has been studied in [27, 28, 29] when Card(A) = 1 and the second momentofisﬁnite. Absolutecontinuityargumentshaveoftenbeenusedtoderiveinvariance principlesforrandomtreesandforests,seee.g. [8,12,24,22]. Let us now discuss the relationship between the present work and Rizzolo’s recent artic”