Uniform infinite planar quadrangulations with a boundary

DOI10.1002/rsa.20531zbMath1351.60011arXiv1202.5452OpenAlexW2055911251MaRDI QIDQ3192371

Grégory Miermont, Nicolas Curien

Publication date: 12 October 2015

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.5452

zbMATH Keywords

stable lawsquadrangulationsself-avoiding walkrandom planar mapslocal limits

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Enumeration in graph theory (05C30) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (22)

Liouville quantum gravity on the unit disk ⋮ Limits of the boundary of random planar maps ⋮ Simple random walk on the uniform infinite planar quadrangulation: Subdiffusivity via pioneer points ⋮ Uniform infinite half-planar quadrangulations with skewness ⋮ Simple peeling of planar maps with application to site percolation ⋮ Classification of scaling limits of uniform quadrangulations with a boundary ⋮ Separating cycles and isoperimetric inequalities in the uniform infinite planar quadrangulation ⋮ Self-Avoiding Walks on the UIPQ ⋮ On site percolation in random quadrangulations of the half-plane ⋮ How fast planar maps get swallowed by a peeling process ⋮ The incipient infinite cluster of the uniform infinite half-planar triangulation ⋮ Brownian geometry ⋮ Unimodular hyperbolic triangulations: circle packing and random walk ⋮ A glimpse of the conformal structure of random planar maps ⋮ The generating function of planar Eulerian orientations ⋮ Spine representations for non-compact models of random geometry ⋮ Geodesic rays in the uniform infinite half-planar quadrangulation return to the boundary ⋮ Recurrence of the uniform infinite half-plane map via duality of resistances ⋮ Percolations on random maps. I: Half-plane models ⋮ Scaling limit of random planar quadrangulations with a boundary ⋮ Scaling limits of random planar maps with a unique large face ⋮ Classification of half-planar maps

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