publication . Preprint . Article . Other literature type . 2019

Determinantal spanning forests on planar graphs

Richard Kenyon;
Open Access English
  • Published: 01 Mar 2019
We generalize the uniform spanning tree to construct a family of determinantal measures on essential spanning forests on periodic planar graphs in which every component tree is bi-infinite. Like the uniform spanning tree, these measures arise naturally from the Laplacian on the graph. ¶ More generally, these results hold for the “massive” Laplacian determinant which counts rooted spanning forests with weight $M$ per finite component. These measures typically have a form of conformal invariance, unlike the usual rooted spanning tree measure. We show that the spectral curve for these models is always a simple Harnack curve; this fact controls the decay of edge-edg...
free text keywords: Mathematics - Probability, 82B20, 60Cxx, Statistics, Probability and Uncertainty, Statistics and Probability, Graph Laplacian, spanning forest, determinantal process, limit shape, 82B20, Minimum spanning tree, Discrete mathematics, Spanning tree, Euclidean minimum spanning tree, Connected dominating set, Loop-erased random walk, Combinatorics, k-minimum spanning tree, Minimum degree spanning tree, Mathematics, Laplacian matrix
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Funded by
NSF| Integrability and limit shapes in the two-dimensional Ising model and related models
  • Funder: National Science Foundation (NSF)
  • Project Code: 1208191
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences

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