Schramm's proof of Watts' formula

DOI10.1214/11-AOP652zbMath1238.60089arXiv1003.3271MaRDI QIDQ651006

Scott Sheffield, David Bruce Wilson

Publication date: 8 December 2011

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.3271

zbMATH Keywords

percolationCardy's formulaSchramm-Loewwner equation

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

Related Items (10)

Pivotal, cluster, and interface measures for critical planar percolation ⋮ Boundary correlations in planar LERW and UST ⋮ A proof of factorization formula for critical percolation ⋮ Baxter permuton and Liouville quantum gravity ⋮ Integrability of SLE via conformal welding of random surfaces ⋮ A formula for crossing probabilities of critical systems inside polygons ⋮ Conformally invariant scaling limits in planar critical percolation ⋮ Oded Schramm: from circle packing to SLE ⋮ Critical percolation: The expected number of clusters in a rectangle ⋮ Toward a conformal field theory for Schramm-Loewner evolutions

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Contour lines of the two-dimensional discrete Gaussian free field
• Multiple Schramm-Loewner evolutions and statistical mechanics martingales
• Euler integrals for commuting SLEs
• Excursion decompositions for SLE and Watts' crossing formula
• Reversibility of chordal SLE
• On the universality of crossing probabilities in two-dimensional percolation
• On crossing event formulas in critical two-dimensional percolation
• Conformal invariance of planar loop-erased random walks and uniform spanning trees.
• Reflected planar Brownian motions, intertwining relations and crossing probabilities
• Harmonic explorer and its convergence to \(\text{SLE}_4\)
• Basic properties of SLE
• Critical percolation exploration path and \(\mathrm{SLE}_{6}\): a proof of convergence
• Critical percolation in finite geometries
• Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
• A crossing probability for critical percolation in two dimensions
• Percolation crossing formulae and conformal field theory

This page was built for publication: Schramm's proof of Watts' formula