The scaling limit of loop-erased random walk in three dimensions
نویسنده
چکیده
Loop-erased random walk is a model for a random simple (i.e. non-selfintersecting) path created by taking a random walk and, whenever it hits itself, deleting the resulting loop and continuing. We will explain why this model is interesting and why scaling limits are interesting, and then go on to describe the proof (that the limit exists), as time will permit.
منابع مشابه
Scaling Limit of Loop Erased Random Walk — a Naive Approach
We give an alternative proof of the existence of the scaling limit of loop-erased random walk which does not use Löwner’s differential equation.
متن کاملConvergence of loop-erased random walk in the natural parameterization
We prove that loop-erased random walk parametrized by renormalized length converges in the lattice size scaling limit to SLE2 parametrized by Minkowski content.
متن کاملScaling Limits of the Uniform Spanning Tree and Loop-erased Random Walk on Finite Graphs
Let x and y be chosen uniformly in a graph G. We find the limiting distribution of the length of a loop-erased random walk from x to y on a large class of graphs that include the torus Zn for d ≥ 5. Moreover, on this family of graphs we show that a suitably normalized finite-dimensional scaling limit of the uniform spanning tree is a Brownian continuum random tree.
متن کاملScaling Limit of Loop-erased Random Walk
The loop-erased random walk (LERW) was first studied in 1980 by Lawler as an attempt to analyze self-avoiding walk (SAW) which provides a model for the growth of a linear polymer in a good solvent. The self-avoiding walk is simply a path on a lattice that does not visit the same site more than once. Proving things about the collection of all such paths is a formidable challenge to rigorous math...
متن کاملLoop-Erased Random Walk and Poisson Kernel on Planar Graphs
Lawler, Schramm and Werner showed that the scaling limit of the loop-erased random walk on Z2 is SLE2. We consider scaling limits of the loop-erasure of random walks on other planar graphs (graphs embedded into C so that edges do not cross one another). We show that if the scaling limit of the random walk is planar Brownian motion, then the scaling limit of its loop-erasure is SLE2. Our main co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005