The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus

DOI10.1007/s00440-008-0149-7zbMath1183.60039arXivmath/0602515OpenAlexW2072536307MaRDI QIDQ2391165

Jason Ross Schweinsberg

Publication date: 24 July 2009

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602515

zbMATH Keywords

loop-erased random walkcontinuum random treeuniform spanning tree

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Sums of independent random variables; random walks (60G50) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (12)

Spatial networks and percolation. Abstracts from the workshop held January 17--23, 2021 (hybrid meeting) ⋮ Loop-erased partitioning of a graph: mean-field analysis ⋮ The diameter of uniform spanning trees in high dimensions ⋮ Random graph asymptotics on high-dimensional tori ⋮ Finite size scaling of the 5D Ising model with free boundary conditions ⋮ Logarithmic corrections to scaling in the four-dimensional uniform spanning tree ⋮ Models of random subtrees of a graph ⋮ The GHP scaling limit of uniform spanning trees in high dimensions ⋮ Spectral dimension and random walks on the two dimensional uniform spanning tree ⋮ Loop-erased random walk on finite graphs and the Rayleigh process ⋮ Interlacements and the wired uniform spanning forest ⋮ Universality of high-dimensional spanning forests and sandpiles

Cites Work

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• The continuum random tree. I
• Loop-erased random walk on finite graphs and the Rayleigh process
• Choosing a spanning tree for the integer lattice uniformly
• Escape probabilities for slowly recurrent sets
• The logarithmic correction for loop-erased walk in four dimensions
• Markov chain intersections and the loop-erased walk
• Conformal invariance of planar loop-erased random walks and uniform spanning trees.
• The continuum random tree. III
• The scaling limit of loop-erased random walk in three dimensions
• Loop-erased random walk on a torus in dimensions 4 and above

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