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Article overview
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The Green's function on the double cover of the grid and application to the uniform spanning tree trunk | Richard W. Kenyon
; David B. Wilson
; | Date: |
17 Aug 2017 | Abstract: | We show how to compute the local statistics of the "trunk" of the uniform
spanning tree on the square lattice, i.e., the limiting probabilities of
cylinder events conditional on the path connecting far away points passing
through a specified edge. We also show how to compute the local statistics of
large-scale triple points of the uniform spanning tree, where the trunk
branches. The method reduces the problem to a dimer system with isolated
monomers, and we compute the inverse Kasteleyn matrix using the Green’s
function on the double cover of the square lattice. For the trunk, the
probabilities of cylinder events are in ${mathbb Q}[sqrt{2}]$, while for the
triple points the probabilities are in ${mathbb Q}[1/pi]$. | Source: | arXiv, 1708.5381 | Services: | Forum | Review | PDF | Favorites |
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