Liouville metric of star-scale invariant fields: tails and Weyl scaling

DOI10.1007/s00440-019-00919-zzbMath1434.60284arXiv1809.02607OpenAlexW2890181357MaRDI QIDQ2291692

Julien Dubédat, Hugo Falconet

Publication date: 31 January 2020

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

Full work available at URL: https://arxiv.org/abs/1809.02607

zbMATH Keywords

tail estimateslog-correlated Gaussian fieldsLiouville metricRusso-Seymour-Welsh estimatesWeyl scaling

Mathematics Subject Classification ID

Random fields (60G60) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (12)

Tightness of Liouville first passage percolation for \(\gamma \in (0,2)\) ⋮ Subsequential scaling limits for Liouville graph distance ⋮ Tightness of supercritical Liouville first passage percolation ⋮ Introduction to the Liouville quantum gravity metric ⋮ Weak LQG metrics and Liouville first passage percolation ⋮ Existence and uniqueness of the Liouville quantum gravity metric for \(\gamma \in (0, 2)\) ⋮ Bounds for distances and geodesic dimension in Liouville first passage percolation ⋮ Conformal covariance of the Liouville quantum gravity metric for \(\gamma\in (0,2)\) ⋮ Volume of metric balls in Liouville quantum gravity ⋮ The Tutte embedding of the Poisson-Voronoi tessellation of the Brownian disk converges to \(\sqrt{8/3}\)-Liouville quantum gravity ⋮ The dimension of the boundary of a Liouville quantum gravity metric ball ⋮ Heat kernel for Liouville Brownian motion and Liouville graph distance

Cites Work

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• On Gaussian multiplicative chaos
• Crossing probabilities for Voronoi percolation
• Uniqueness and universality of the Brownian map
• The Brownian map is the scaling limit of uniform random plane quadrangulations
• Quantum Loewner evolution
• Liouville quantum gravity and KPZ
• Gaussian multiplicative chaos revisited
• Oriented percolation in two dimensions
• Positively correlated normal variables are associated
• Non-universality for first passage percolation on the exponential of log-correlated Gaussian fields
• On the Liouville heat kernel for \(k\)-coarse MBRW
• Lognormal \(\star\)-scale invariant random measures
• The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds
• Liouville quantum gravity and the Brownian map II: geodesics and continuity of the embedding
• Liouville quantum gravity and the Brownian map. I: The \(\text{QLE}(8/3,0)\) metric
• Decompositions of log-correlated fields with applications
• Heat kernel for Liouville Brownian motion and Liouville graph distance
• The topological structure of scaling limits of large planar maps
• Liouville first-passage percolation: subsequential scaling limits at high temperature
• An introduction to infinite-dimensional analysis
• An elementary approach to Gaussian multiplicative chaos
• Liouville quantum gravity and the Brownian map. III: The conformal structure is determined
• 50 Years of First-Passage Percolation
• Upper Bounds on Liouville First‐Passage Percolation and Watabiki's Prediction
• Random Fields and Geometry
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Complex analysis. Transl. from the German by Dan Fulea

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