Recent progress on loop-erased random walk in three dimensions

Loop-erased random walk (LERW) is a model for a random simple path, which is created by running a simple random walk and, whenever the random walk hits its path, removing the resulting loop and continuing. LERW was originally introduced by Greg Lawler in 1980. Since then, it has been studied extensively both in mathematics and physics literature. Indeed, LERW has a strong connection with other models in statistical physics, especially the uniform spanning tree which arises in statistical physics in conjunction with the Potts model. In this talk, I will talk about some recent progress on LERW while focusing on the three-dimensional case.

This is joint work with Xinyi Li.