Brownian motion correlation in the peanosphere for \(\kappa>8\)

DOI10.1214/16-AIHP774zbMath1388.60143arXiv1510.04687OpenAlexW2963105364MaRDI QIDQ1700395

Xin Sun, Ewain Gwynne, Jason Miller, Nina Holden

Publication date: 5 March 2018

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.04687

zbMATH Keywords

Schramm-Loewner evolutionLiouville quantum gravitypeanosphere

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

Related Items (18)

Chordal \(\mathrm{SLE}_6\) explorations of a quantum disk ⋮ Liouville quantum gravity and the Brownian map. III: The conformal structure is determined ⋮ An almost sure KPZ relation for SLE and Brownian motion ⋮ Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for \(\kappa>8\) ⋮ Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity ⋮ Bipolar orientations on planar maps and \(\mathrm{SLE}_{12}\) ⋮ The Minkowski content measure for the Liouville quantum gravity metric ⋮ Equivalence of Liouville measure and Gaussian free field ⋮ Nesting statistics in the \(O(n)\) loop model on random planar maps ⋮ What is a random surface? ⋮ A distance exponent for Liouville quantum gravity ⋮ The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds ⋮ The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity ⋮ SLE as a mating of trees in Euclidean geometry ⋮ Dimension transformation formula for conformal maps into the complement of an SLE curve ⋮ Liouville quantum gravity surfaces with boundary as matings of trees ⋮ Tree-decorated planar maps ⋮ Liouville quantum gravity spheres as matings of finite-diameter trees

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Imaginary geometry. I: Interacting SLEs
• Conformal weldings of random surfaces: SLE and the quantum gravity zipper
• Imaginary geometry. III: Reversibility of \(\mathrm{SLE}_\kappa\) for \(\kappa \in (4,8)\)
• Uniqueness and universality of the Brownian map
• The Brownian map is the scaling limit of uniform random plane quadrangulations
• Gaussian multiplicative chaos and applications: a review
• Quantum Loewner evolution
• Quantum gravity and inventory accumulation
• Liouville quantum gravity and KPZ
• Imaginary geometry. II: Reversibility of \(\operatorname{SLE}_{\kappa}(\rho_{1};\rho_{2})\) for \(\kappa\in(0,4)\)
• The continuum random tree. I
• Exploration trees and conformal loop ensembles
• Excursions in a cone for two-dimensional Brownian motion
• Scaling limits of loop-erased random walks and uniform spanning trees
• Imaginary geometry. IV: Interior rays, whole-plane reversibility, and space-filling trees
• Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map. I: Cone times
• Liouville quantum gravity and the Brownian map II: geodesics and continuity of the embedding
• An almost sure KPZ relation for SLE and Brownian motion
• Liouville quantum gravity spheres as matings of finite-diameter trees
• The continuum random tree. III
• Basic properties of SLE
• Critical exponents on Fortuin-Kasteleyn weighted planar maps
• Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for \(\kappa>8\)
• Bipolar orientations on planar maps and \(\mathrm{SLE}_{12}\)
• SLE coordinate changes
• Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map. II: Local estimates and empty reduced word exponent
• An axiomatic characterization of the Brownian map
• Liouville quantum gravity and the Brownian map. III: The conformal structure is determined
• On the Hausdorff dimension of Brownian cone points
• Liouville quantum gravity as a mating of trees

This page was built for publication: Brownian motion correlation in the peanosphere for \(\kappa>8\)