Random-cluster measures and uniform spanning trees

The Random Walk Construction of Uniform Spanning Trees and Uniform Labelled Trees

A random walk on a finite graph can be used to construct a uniform random spanning tree. We show how random walk techniques can be applied to the study of several properties of the uniform random spanning tree: the proportion of leaves, the distribution of degrees, and the diameter.

Non-Uniform Random Spanning Trees on Weighted Graphs

We study random walks on undirected graphs with weighted edges. Our main result shows that any spanning tree deened by the edges corresponding to a rst visit of a vertex, appears with a probability proportional to its weight, which is the product of the weights of its edges. This provides an algorithm for generating non uniform random spanning trees in a weighted graph. The technique used here ...

Generating Random Spanning Trees

This paper describes a probabilistic algorithm that, given a connected, undirected graph G with n vertices, produces a spanning tree of G chosen uniformly at random among the spanning trees of G. The expected running time is O(n logn) per generated tree for almost all graphs, and O(n3) for the worst graphs. Previously known deterministic algorithms and much more complicated and require O(n3) ti...

Generating Random Spanning Trees

Random Walks and Random Spanning Trees

We explore algorithms for generating random spanning trees. We first study an algorithm that was developed independently by David Alduous [1] and Andrei Broder [2]. The algorithm uses a a simple random walk in which edges that correspond to the first visit to vertices are added to the spanning tree. Analysis was inspired by Andrei Broder’s paper. Additionally, we study an algorithm by David Wil...