I am working on a problem with a Loop Erased Random Walk used to create random spanning trees from a graph. The problem has many parts, but there are two hints to help with the more complicated problems. The hints are essentially:
1.Figure out the probability that any given edge will be contained in the uniform spanning tree.
2.Figure out the probability that an edge is added in a given direction (given the below algorithm) in the uniform spanning tree.
I have been working through this for hours and hours now and have hit a wall. Any tips towards figuring these out would be extremely helpful as I have no idea where to begin at this point.
Random Walk Algorithm:
Pick an arbitrary root in V. Begin at root and traverse graph randomly. Whenever we reach a vertex that has not yet been added to the tree, we add the edge that we used to reach that vertex to our spanning tree