Loop-erased random walk

Summary

A loop-erased random walk is the simple path obtained from a random walk by erasing its loops in the order in which they are created. It is a random self-avoiding path, but its law differs from the uniform self-avoiding walk. Through Wilson's algorithm it is the building block of the uniform spanning tree of a graph. In the plane its scaling limit is the Schramm–Loewner evolution with parameter $2$.