The conformal loop ensemble nesting field

DOI10.1007/s00440-014-0604-6zbMath1334.60038arXiv1401.0218OpenAlexW3101467048MaRDI QIDQ892166

Samuel S. Watson, Jason Miller, David Bruce Wilson

Publication date: 18 November 2015

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

Full work available at URL: https://arxiv.org/abs/1401.0218

zbMATH Keywords

almost sure convergenceGaussian free fieldconformal loop ensemblenesting fieldrandom conformally invariant limit

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Geometric probability and stochastic geometry (60D05) Strong limit theorems (60F15) Ergodicity, mixing, rates of mixing (37A25) Large deviations (60F10) Functional limit theorems; invariance principles (60F17) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

Related Items

The random pseudo-metric on a graph defined via the zero-set of the Gaussian free field on its metric graph ⋮ A characterisation of the Gaussian free field ⋮ An almost sure KPZ relation for SLE and Brownian motion ⋮ Thick points of the planar GFF are totally disconnected for all \(\gamma \neq 0\) ⋮ Brownian half‐plane excursion and critical Liouville quantum gravity ⋮ Nesting statistics in the \(O(n)\) loop model on random planar maps ⋮ Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman ⋮ Limit theorems for critical first-passage percolation on the triangular lattice ⋮ Level lines of Gaussian free field. I: Zero-boundary GFF. ⋮ Almost sure multifractal spectrum of Schramm-Loewner evolution ⋮ The expectation value of the number of loops and the left-passage probability in the double-dimer model

Cites Work

• Unnamed Item
• Unnamed Item
• Extreme nesting in the conformal loop ensemble
• The self-dual point of the two-dimensional random-cluster model is critical for \(q \geqslant 1\)
• The nested simple conformal loop ensembles in the Riemann sphere
• Conformal radii for conformal loop ensembles
• Partial differential equations. I: Basic theory
• Exploration trees and conformal loop ensembles
• A guide to stochastic Löwner evolution and its applications
• Conformal loop ensembles: the Markovian characterization and the loop-soup construction
• Basic properties of SLE
• Stopped Random Walks
• Probability with Martingales
• Thick points for planar Brownian motion and the Erdős-Taylor conjecture on random walk

This page was built for publication: The conformal loop ensemble nesting field