Classification of scaling limits of uniform quadrangulations with a boundary

DOI10.1214/18-AOP1316zbMath1448.60027arXiv1608.01129OpenAlexW2990817043MaRDI QIDQ2189452

Gourab Ray, Grégory Miermont, Erich Baur

Publication date: 15 June 2020

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.01129

zbMATH Keywords

scaling limitGromov-Hausdorff convergencequadrangulationBrownian mapplanar mapBrownian treeBrownian disk

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Random graphs (graph-theoretic aspects) (05C80) Functional limit theorems; invariance principles (60F17)

Related Items (18)

Compact Brownian surfaces ⋮ The Brownian disk viewed from a boundary point ⋮ Liouville quantum gravity and the Brownian map. III: The conformal structure is determined ⋮ Geodesic networks in Liouville quantum gravity surfaces ⋮ The mesoscopic geometry of sparse random maps ⋮ Limits of random tree-like discrete structures ⋮ Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants ⋮ Decorated stable trees ⋮ Local convergence of large random triangulations coupled with an Ising model ⋮ Compact Brownian surfaces. I: Brownian disks ⋮ Brownian geometry ⋮ Liouville quantum gravity surfaces with boundary as matings of trees ⋮ Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense ⋮ Spine representations for non-compact models of random geometry ⋮ The Tutte embedding of the Poisson-Voronoi tessellation of the Brownian disk converges to \(\sqrt{8/3}\)-Liouville quantum gravity ⋮ Metric gluing of Brownian and \(\sqrt{8/3}\)-Liouville quantum gravity surfaces ⋮ The geodesics in Liouville quantum gravity are not Schramm-Loewner evolutions ⋮ Isoperimetric inequalities in the Brownian plane

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geodesics in Brownian surfaces (Brownian maps)
• The hull process of the Brownian plane
• Uniqueness and universality of the Brownian map
• The Brownian map is the scaling limit of uniform random plane quadrangulations
• The Brownian plane
• Compact Brownian surfaces. I: Brownian disks
• Geodesics in large planar maps and in the Brownian map
• Scaling limits for random quadrangulations of positive genus
• The topology of scaling limits of positive genus random quadrangulations
• The continuum random tree. I
• The hyperbolic Brownian plane
• Uniform infinite half-planar quadrangulations with skewness
• Planar maps as labeled mobiles
• Recurrence of distributional limits of finite planar graphs
• Scaling limit of random planar quadrangulations with a boundary
• The continuum random tree. III
• Scaling limit of the uniform infinite half-plane quadrangulation in the Gromov-Hausdorff-Prokhorov-uniform topology
• Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
• Local limit of labeled trees and expected volume growth in a random quadrangulation
• Conditioned Brownian trees
• A view from infinity of the uniform infinite planar quadrangulation
• Planar Maps are Well Labeled Trees
• Uniform infinite planar quadrangulations with a boundary
• Tessellations of random maps of arbitrary genus
• Distance statistics in quadrangulations with a boundary, or with a self-avoiding loop
• Geometry of the uniform infinite half‐planar quadrangulation
• A local limit theorem and loss of rotational symmetry of planar symmetric simple random walk
• Scaling limits of random trees and planar maps
• On the Classification of Noncompact Surfaces
• Markov functions

This page was built for publication: Classification of scaling limits of uniform quadrangulations with a boundary