Random two-component spanning forests
  We study random two-component spanning forests ($2$SFs) of finite graphs, giving formulas for the first and second moments of the sizes of the components, vertex-inclusion probabilities for one or two vertices, and the probability that an edge separates the components. We compute the limit of these quantities when the graph tends to an infinite periodic graph in ${\mathbb R}^d$. 
Adrien Kassel, Richard Kenyon, Wei Wu
math.PR math-ph math.MP