Scaling limits of loop-erased random walks and uniform spanning trees

2000/12/01 by Oded Schramm · 38 citations
Mathematics · Physics and Astronomy · #Combinatorics #Conformal map #Conjecture #Discrete mathematics #Geometry #Invariant (physics) #Limit (mathematics) #Loop-erased random walk #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Plane (geometry) #Random graph #Random walk #Scaling #Scaling limit #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.1007/bf02803524

crossref issued 2000/12/01 · crossref published 2000/12/01 · crossref published-print 2000/12/01 · openalex publication_date 2000/12/01 · crossref created 2008/01/24 · crossref deposited 2020/05/01 · openalex created_date 2025/10/10 · crossref indexed 2026/07/29 · openalex updated_date 2026/08/01

Citations

• Choosing a Spanning Tree for the Integer Lattice Uniformly
• Generating random spanning trees more quickly than the cover time
• Critical percolation in finite geometries
• Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I
• Conformal invariance of domino tiling

Cited by

• Interlacements and the wired uniform spanning forest
• Determinantal correlations of Brownian paths in the plane with nonintersection condition on their loop-erased parts
• An SLE₂ loop measure
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• Slow Convergence of Ising and Spin Glass Models with Well-Separated Frustrated Vertices
• Pivotal, cluster, and interface measures for critical planar percolation
• Conformal invariance and 2𝐷 statistical physics
• Conformal restriction and related questions
• Critical exponents for two-dimensional percolation
• Quantitative noise sensitivity and exceptional times for percolation
• Conformally invariant scaling limits: an overview and a collection of problems
• Conformal invariance of planar loop-erased random walks and uniform spanning trees
• The scaling limit of loop-erased random walk in three dimensions
• The Dimension of the Planar Brownian Frontier is 4/3
• Harmonic Measure and SLE
• Fractal Structure of Isothermal Lines and Loops on the Cosmic Microwave Background
• Commutation relations for Schramm‐Loewner evolutions
• Euler Integrals for Commuting SLEs
• Excursion decompositions for SLE and Watts' crossing formula
• Large deviations of radial SLE_∞
• Stochastic interface dynamics in the Hele-Shaw cell
• The Fractal Dimension of Liouville Quantum Gravity: Universality, Monotonicity, and Bounds
• Duality of critical interfaces in Potts model: numerical check
• Percolation beyond ℤd: The contributions of Oded Schramm
• Values of Brownian intersection exponents III: Two-sided exponents
• Revisiting the combinatorics of the 2D Ising model
• Self-similar but not conformally invariant traces obtained by modified Loewner forces
• Loop-erased random walk and Poisson kernel on planar graphs
• SLE and the free field: Partition functions and couplings
• Dominos and the Gaussian Free Field
• On stochastic evolutions and superconformal field theory
• Higher moments of the natural parameterization for SLE curves
• Conformal Curves on theWO3Surface
• SLE-type growth processes and the Yang–Lee singularity
• Exact Multifractal Spectra for Arbitrary Laplacian Random Walks
• Loop-erased random walk on a percolation cluster: Crossover from Euclidean to fractal geometry
• Oded Schramm: From circle packing to SLE
• Loop-erased random walk [wikipedia]
• Schramm–Loewner evolution [wikipedia]