Uniform spanning tree

2012 ◽  
pp. 21-38
Author(s):  
Geoffrey Grimmett
Keyword(s):  
Spanning Tree ◽  
Uniform Spanning Tree

scholarly journals The Local Limit of the Uniform Spanning Tree on Dense Graphs

2018 ◽  
Vol 173 (3-4) ◽  
pp. 502-545
Author(s):  
Jan Hladký ◽  
Asaf Nachmias ◽  
Tuan Tran
Keyword(s):  
Spanning Tree ◽  
Local Limit ◽  
Uniform Spanning Tree ◽  
Dense Graphs

scholarly journals Scaling limits of the three-dimensional uniform spanning tree and associated random walk

2021 ◽  
Vol 49 (6) ◽  
Author(s):  
O. Angel ◽  
D. A. Croydon ◽  
S. Hernandez-Torres ◽  
D. Shiraishi
Keyword(s):  
Random Walk ◽  
Spanning Tree ◽  
Three Dimensional ◽  
Scaling Limits ◽  
Uniform Spanning Tree

scholarly journals Pfaffian Formulas for Spanning Tree Probabilities

2016 ◽  
Vol 26 (1) ◽  
pp. 118-137 ◽  
Author(s):  
GRETA PANOVA ◽  
DAVID B. WILSON
Keyword(s):  
Line Bundle ◽  
Green’S Function ◽  
Green's Function ◽  
Spanning Tree ◽  
Young Diagrams ◽  
Linear Combinations ◽  
Uniform Spanning Tree

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.

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