Loop Contracting Random Walk
This is a new stochastic process introduced for the first time in a joint work of Gourab Ray and Arnab Sen , titled Loop Contracting Random Walk.
This process is a natural analogue of the loop-erased random walk (which is used to sample the uniform spanning tree). However, instead of erasing loops, the process contracts them.
The process is animated here on a smaller grid. Animation credit: Gourab Ray.
An open question is to prove that this walk is transient on the Euclidean lattice. This has several consequences for the existence of weak limits of the minimum spanning arborescence.