Scaling limits of random trees and planar maps

By Jean-François Le Gall, Grégory Miermont. 2011

135 citations recorded by the source corpus.

These are the notes for a series of lectures given at the Clay Mathematical Institute Summer School in Buzios, July 11 - August 7, 2010. We review some of the recent aspects of scaling limits of random trees and planar maps, in particular via their relations with bijective enumeration and Gromov-Hausdorff convergence.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c2667154301eee7bea8d284d669eb7d8596928d7

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Scaling limits of random planar maps with a unique large face (2012, unknown): “The Annals of Probability 2015, Vol. 43, No. 3, 1045–1081 DOI: 10.1214/13-AOP871 © Institute of Mathematical Statistics, 2015”
Random geometry on the sphere (2014, background): “We refer to [34] for a discussion of scaling limits of labeled plane trees.”
Uniqueness and universality of the Brownian map (2011, background): “The other assertions of the theorem are then obtained in a straightforward way (see Section 3 of [15], or Section 5 of [17]), with the exception of the fact that D(s, t) = 0 implies D∗(s, t) = 0.”
The Brownian map is the scaling limit of uniform random plane quadrangulations (2011, background): “See [17] for a recent survey of the field.”
Gaussian multiplicative chaos and applications: A review (2013, background): “Interestingly, they have also understood that such metrics can be discretized by randomly triangulated surfaces (see [6] for instance), a recent field of mathematical research that culminated with the construction of the so-called Brownian map (see [106, 107, 108, 117]) in the special case of pure g”
The Brownian Plane (2012, methodology): “We then use the convergence towards the Brownian map (6) and Proposition 4 to complete the proof.”
Scaling Limits of Random Graphs from Subcritical Classes (2014, methodology): “Since Aldous’s pioneering work, the CRT has been identified as the limiting object of many different classes of discrete structures, in particular trees, see e.g. Haas and Miermont [16] and references therein, and planar maps, see e.g. Albenque and Marckert [2], Bettinelli [8], Caraceni [9], Curien,”