Loop-erased random walk and Poisson kernel on planar graphs

DOI10.1214/10-AOP579zbMath1234.60036arXiv0809.2643MaRDI QIDQ717878

Amir Yehudayoff, Ariel Yadin

Publication date: 10 October 2011

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

Full work available at URL: https://arxiv.org/abs/0809.2643

zbMATH Keywords

planar graphsPoisson kernelSchramm-Loewner evolutionloop-erased random walk

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Functional limit theorems; invariance principles (60F17) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

Related Items (10)

Dimers and imaginary geometry ⋮ Boundary correlations in planar LERW and UST ⋮ Quantitative Russo-Seymour-Welsh for random walk on random graphs and decorrelation of uniform spanning trees ⋮ UST branches, martingales, and multiple SLE(2) ⋮ Recent progress on the random conductance model ⋮ Characterisation of planar Brownian multiplicative chaos ⋮ Loop-erased walks and random matrices ⋮ On the convergence of massive loop-erased random walks to massive SLE(2) curves ⋮ The Tutte embedding of the Poisson-Voronoi tessellation of the Brownian disk converges to \(\sqrt{8/3}\)-Liouville quantum gravity ⋮ Asymptotics of height change on toroidal Temperleyan dimer models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quenched invariance principle for simple random walk on percolation clusters
• A self-avoiding random walk
• Weak convergence of a random walk in a random environment
• Scaling limits of loop-erased random walks and uniform spanning trees
• Conformal invariance of planar loop-erased random walks and uniform spanning trees.
• Basic properties of SLE
• The scaling limit of loop-erased random walk in three dimensions
• Brownian Motion

This page was built for publication: Loop-erased random walk and Poisson kernel on planar graphs