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Pfaffian Formulas for Spanning Tree Probabilities

Part of: Equilibrium statistical mechanics Graph theory Combinatorial probability

Published online by Cambridge University Press:  30 May 2016

GRETA PANOVA  and
DAVID B. WILSON
GRETA PANOVA
Affiliation:
Mathematics Department, University of Pennsylvania, Philadelphia, PA 19104, USA (e-mail: panova@math.upenn.edu), http://www.math.upenn.edu/~panova/
DAVID B. WILSON
Affiliation:
Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA (e-mail: David.Wilson@microsoft.com), http://dbwilson.com
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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.

MSC classification

Primary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 05C05: Trees
Secondary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.) 05C10: Planar graphs; geometric and topological aspects of graph theory 60C05: Combinatorial probability
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 1 , January 2017 , pp. 118 - 137
Copyright
Copyright © Cambridge University Press 2016 

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