On the rate of convergence of loop-erased random walk to \(\mathrm{SLE}_{2}\)

DOI10.1007/s00220-013-1666-5zbMath1268.60117arXiv0911.3988OpenAlexW1995276970MaRDI QIDQ1942285

Christian Beneš, Fredrik Johansson Viklund, Michael J. Kozdron

Publication date: 18 March 2013

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.3988

zbMATH Keywords

rate of convergenceBrownian motionloop-erased random walkSchramm-Loewner evolution (SLE)

Mathematics Subject Classification ID

Gaussian processes (60G15) Sums of independent random variables; random walks (60G50) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Other physical applications of random processes (60K40) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Functional limit theorems; invariance principles (60F17)

Related Items (12)

Convergence of loop-erased random walk in the natural parameterization ⋮ Rate of Convergence of Critical Interfaces to SLE Curves ⋮ Scaling limit of the loop-erased random walk Green's function ⋮ Perturbations of multiple Schramm-Loewner evolution with two non-colliding Dyson Brownian motions ⋮ Green's functions for chordal SLE curves ⋮ Some partial results on the convergence of loop-erased random walk to \(\mathrm{SLE}(2)\) in the natural parametrization ⋮ A support theorem for SLE curves ⋮ The difference between a discrete and continuous harmonic measure ⋮ Convergence rates for loop-erased random walk and other Loewner curves ⋮ Transition probabilities for infinite two-sided loop-erased random walks ⋮ Rates of convergence for the planar discrete Green's function in pacman domains ⋮ On the rate of convergence for critical crossing probabilities

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