Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on planar graphs

DOI10.1090/S0894-0347-2014-00819-5zbMath1327.60033arXiv1107.3377OpenAlexW2161939735MaRDI QIDQ5264116

David Bruce Wilson, Richard W. Kenyon

Publication date: 20 July 2015

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.3377

zbMATH Keywords

abelian sandpile modelloop-erased random walkuniform spanning treevector-bundle Laplacian

Mathematics Subject Classification ID

Trees (05C05) Combinatorial probability (60C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (23)

Fundamental constants in the theory of two-dimensional uniform spanning trees ⋮ Scaling limit of the loop-erased random walk Green's function ⋮ The Sandpile Cellular Automaton ⋮ Some partial results on the convergence of loop-erased random walk to \(\mathrm{SLE}(2)\) in the natural parametrization ⋮ Boundary correlations in planar LERW and UST ⋮ The Space of Circular Planar Electrical Networks ⋮ Universality conjectures for activated random walk ⋮ Sandpile probabilities on triangular and hexagonal lattices ⋮ Pfaffian Formulas for Spanning Tree Probabilities ⋮ Laplacian growth, sandpiles, and scaling limits ⋮ Asymptotic height distribution in high-dimensional sandpiles ⋮ The Green's function on the double cover of the grid and application to the uniform spanning tree trunk ⋮ Strongly correlated random interacting processes. Abstracts from the workshop held January 28 -- February 3, 2018 ⋮ The bundle Laplacian on discrete tori ⋮ Multipoint correlators in the Abelian sandpile model ⋮ Schramm’s formula for multiple loop-erased random walks ⋮ Toppling and height probabilities in sandpiles ⋮ Sandpile models ⋮ Diffuse scattering on graphs ⋮ Transfer current and pattern fields in spanning trees ⋮ Laminations of a graph on a pair of pants ⋮ Threshold state and a conjecture of Poghosyan, Poghosyan, Priezzhev and Ruelle ⋮ Dyck tilings, increasing trees, descents, and inversions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Proofs of two conjectures of Kenyon and Wilson on Dyck tilings
• Fully packed loops in a triangle: matchings, paths and puzzles
• Double-dimer pairings and skew Young diagrams
• Spanning forests and the vector bundle Laplacian
• Potential kernel for two-dimensional random walk
• The cycle lemma and some applications
• Approximation of conformal mappings by circle patterns
• Circular planar graphs and resistor networks
• Choosing a spanning tree for the integer lattice uniformly
• Perplexing problems in probability. Festschrift in honor of Harry Kesten
• Planar electric networks. I
• The Laplacian and Dirac operators on critical planar graphs
• An asymptotic expansion for the discrete harmonic potential
• The cube recurrence
• Uniform spanning forests
• Conformal invariance of planar loop-erased random walks and uniform spanning trees.
• Planar electric networks. II
• Path representation of maximal parabolic Kazhdan-Lusztig polynomials.
• Dyck tilings, increasing trees, descents, and inversions
• Determinants of Laplacians on graphs
• Moduli spaces of local systems and higher Teichmüller theory
• Correlations between eigenvalues of a random matrix
• A problem of arrangements
• Loop-erased walks and total positivity
• Long-range properties of spanning trees
• The looping constant of Z^d
• Inverse Problem in Cylindrical Electrical Networks
• Boundary partitions in trees and dimers
• Self-organized criticality
• Random Walk: A Modern Introduction
• Über einige lineare partielle Differenzengleichungen mit konstanten Koeffizienten
• The asymptotic determinant of the discrete Laplacian

This page was built for publication: Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on planar graphs