Pfaffian formulas for spanning tree probabilities

Abstract

We show that certain topologically defined uniform spanning tree probabilities for graphs embedded in an annulus can be computed as linear combinations of Pfaffians of matrices involving the line-bundle Green's function, where the coefficients count cover-inclusive Dyck tilings of skew Young diagrams.

18 pages

References in corpus (3)

• Spanning forests and the vector bundle Laplacian
• Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on planar graphs
• Dyck tilings, increasing trees, descents, and inversions

Cited by in corpus (3)

• Boundary correlations in planar LERW and UST
• Schramm's formula for multiple loop-erased random walks
• Sandpile probabilities on triangular and hexagonal lattices