Long-range properties of spanning trees

By Richard Kenyon. 2000

52 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/43897c4441ef40e2a7f7b1ec7722175a7f490439

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

SLE coordinate changes (2005, methodology): “The exponent of (n 2 − 1)/4 agrees with the value computed in [Dup87, Ken00 ].”
Conformal invariance of planar loop-erased random walks and uniform spanning trees (2001, methodology): “Cauchy-Riemann equations, Richard Kenyon [Ken00a, Ken00b ] rigorously established the values of various critical exponents predicted for the LERW [GB90, Maj92, Dup92] in two dimensions.”
Random planar curves and Schramm-Loewner evolutions (2003, methodology): “The fourth chapter is devoted to some special properties of SLE that hold for some special values of the parameter κ: The locality property for SLE6, and the restriction property for SLE8/3.”
Uniform spanning forests (2001, background): “For the network with unit conductances on a finitely generated group G, Kesten (1959) showed that ρ(G) = 1 iff G is amenable.”
Universality in the 2D Ising model and conformal invariance of fermionic observables (2009, methodology): “Kenyon’s dimer results had corollaries [26] for the Uniform Spanning Tree (and the Loop Erased Random Walk).”
Values of Brownian intersection exponents, II: Plane exponents (2000, background): “For instance, the definition of loop-erased random walks suggests that the number of vertices in the loop-erasure of an N2 step walk is roughly N2−ν(2,1) = N5/4 (loosely speaking, in order for one of the N2 steps of the simple random walk to remain in the loop-erasure, the future of the random walk ”
Two-Dimensional Critical Percolation: The Full Scaling Limit (2006, background): “These new developments came on the heels of interesting results on the scaling limits of discrete models (see, e.g., the work of Aizenman [1, 2], Benjamini‐Schramm [8], Aizenman‐Burchard [3], Aizenman‐Burchard‐Newman‐Wilson [4], Aizenman‐ Duplantier‐Aharony [5] and Kenyon [ 18 , 19]) but they differ”