Random two-component spanning forests

Abstract

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 ${\mathbb{R}}^d$.

References in corpus (6)

• Spanning forests and the vector bundle Laplacian
• Boundary Partitions in Trees and Dimers
• Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on planar graphs
• Random curves on surfaces induced from the Laplacian determinant
• The looping rate and sandpile density of planar graphs
• The looping constant of Z^d

Cited by in corpus (3)

• Random curves on surfaces induced from the Laplacian determinant
• Tree formulas, mean first passage times and Kemeny's constant of a Markov chain
• Sandpiles and unicycles on random planar maps