The distance exponent for Liouville first passage percolation is positive

DOI10.1007/S00440-021-01093-XzbMath1480.60289arXiv2005.13570OpenAlexW3211223797MaRDI QIDQ2067663

Ewain Gwynne, Jian Ding, Avelio Sepúlveda

Publication date: 18 January 2022

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

Full work available at URL: https://arxiv.org/abs/2005.13570

Mathematics Subject Classification ID

Random fields (60G60) Geometric probability and stochastic geometry (60D05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

Related Items (4)

Tightness of supercritical Liouville first passage percolation ⋮ Uniqueness of the critical and supercritical Liouville quantum gravity metrics ⋮ Regularity and confluence of geodesics for the supercritical Liouville quantum gravity metric ⋮ What is a random surface?

Cites Work

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• Liouville quantum gravity on the Riemann sphere
• Crossing probabilities for Voronoi percolation
• Topics in occupation times and Gaussian free fields
• Liouville quantum gravity and KPZ
• From loop clusters and random interlacements to the free field
• The geodesics in Liouville quantum gravity are not Schramm-Loewner evolutions
• Percolation for level-sets of Gaussian free fields on metric graphs
• Tightness of Liouville first passage percolation for \(\gamma \in (0,2)\)
• The Brunn-Minkowski inequality in Gauss space
• Chemical distances for percolation of planar Gaussian free fields and critical random walk loop soups
• Two-valued local sets of the 2D continuum Gaussian free field: connectivity, labels, and induced metrics
• The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds
• Scaling limits of crossing probabilities in metric graph GFF
• The first passage sets of the 2D Gaussian free field: convergence and isomorphisms
• Liouville quantum gravity with matter central charge in (1, 25): a probabilistic approach
• 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
• Comparison of discrete and continuum Liouville first passage percolation
• Convergence in Law of the Maximum of the Two‐Dimensional Discrete Gaussian Free Field
• Random Surfaces and Liouville Quantum Gravity
• Random Fields and Geometry

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