Limits of the boundary of random planar maps

DOI10.1007/s00440-017-0820-yzbMath1400.05213arXiv1704.01950OpenAlexW2606486581MaRDI QIDQ1626619

Loïc Richier

Publication date: 21 November 2018

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.01950

zbMATH Keywords

Boltzmann planar maps

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (8)

Simple peeling of planar maps with application to site percolation ⋮ Infinite stable looptrees ⋮ A phase transition in block-weighted random maps ⋮ On random trees and forests ⋮ The boundary of random planar maps via looptrees ⋮ Duality of random planar maps via percolation ⋮ Brownian motion on stable looptrees ⋮ Stable shredded spheres and causal random maps with large faces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The peeling process of infinite Boltzmann planar maps
• Generalized multicritical one-matrix models
• Uniqueness and universality of the Brownian map
• The Brownian map is the scaling limit of uniform random plane quadrangulations
• Simply generated trees, conditioned Galton-Watson trees, random allocations and condensation
• Quantum gravity and inventory accumulation
• Geometry of infinite planar maps with high degrees
• Geodesics in large planar maps and in the Brownian map
• Scaling limits of random planar maps with large faces
• Condensation in nongeneric trees
• Local limits of conditioned Galton-Watson trees: the condensation case
• Percolation on random triangulations and stable looptrees
• The continuum random tree. I
• Limit of normalized quadrangulations: the Brownian map
• Random trees and applications
• Scaling limits of bipartite planar maps are homeomorphic to the 2-sphere
• Radius and profile of random planar maps with faces of arbitrary degrees
• Arbres et processus de Galton-Watson. (Trees and Galton-Watson processes)
• Subdiffusive behavior of random walk on a random cluster
• A limit theorem for the contour process of conditioned Galton-Watson trees
• Uniform infinite half-planar quadrangulations with skewness
• Local convergence of large critical multi-type Galton-Watson trees and applications to random maps
• Planar maps as labeled mobiles
• Probabilistic and fractal aspects of Lévy trees
• Planar diagrams
• 45th seminar on probability. Including papers of the conference on stochastic filtrations, Strasbourg, France, September 20--22, 2011
• Limit theorems for conditioned non-generic Galton-Watson trees
• Random walk on random infinite looptrees
• Scaling limits of random planar maps with a unique large face
• The continuum random tree. III
• The topological structure of scaling limits of large planar maps
• Critical exponents on Fortuin-Kasteleyn weighted planar maps
• Basic properties of the infinite critical-FK random map
• Invariance principles for random bipartite planar maps
• Random stable looptrees
• Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map. II: Local estimates and empty reduced word exponent
• Local limits of conditioned Galton-Watson trees: the infinite spine case
• Probability on Trees and Networks
• More on theO(n) model on random maps via nested loops: loops with bending energy
• A recursive approach to theO(n) model on random maps via nested loops
• Uniform infinite planar quadrangulations with a boundary
• The CRT is the scaling limit of random dissections
• Distance statistics in quadrangulations with a boundary, or with a self-avoiding loop
• Loop models on random maps via nested loops: the case of domain symmetry breaking and application to the Potts model
• Scaling limits of random bipartite planar maps with a prescribed degree sequence

This page was built for publication: Limits of the boundary of random planar maps