In mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics, physics and quantum field theory. It is intimately connected to …

The relationship between the loop-erased walk and the Laplacian random walk is discussed. Wilson's algorithm to generate spanning trees is discussed in Section 4.4.

We will not try to cover everything about loop-erased random walk (LERW), but rather focus on some of the key properties. We start by reviewing some of the basic facts about LERW.

Sep 1, 2019 · A loop-erased random walk (LERW) is defined as the trajectory of a random walk (RW) in which any loop is erased as soon as it is formed [2]. An example is shown on Fig. 1, …

Due to the well-known correspondence with paths in spanning trees [43, 52], the formula also holds for loop-erased random walks. We compute several explicit expressions in the scaling …

May 9, 2025 · This study delves into the behavior and capacity of loop-erased random walks in various dimensions. Loop-erased random walk (LERW) is a fancy way of...

The loop-erased random walk (LERW) in Z4 is the process obtained by erasing loops chronologically for a simple random walk. We prove that the escape probability of the LERW …

by Jason Schweinsberg University of California at San Diego Outline of Talk The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus

Loop-Erased Random Walk In this chapter, we define and explore the loop-erased random walk (LERW) and show how the LERW relates to the uniform spanning trees (UST).

In mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics, physics and quantum field theory. It is intimately connected to …