Boundary correlations in planar LERW and UST

Abstract

We find explicit formulas for the probabilities of general boundary visit events for planar loop-erased random walks, as well as connectivity events for branches in the uniform spanning tree. We show that both probabilities, when suitably renormalized, converge in the scaling limit to conformally covariant functions which satisfy partial differential equations of second and third order, as predicted by conformal field theory. The scaling limit connectivity probabilities also provide formulas for the pure partition functions of multiple ${\mathrm{SLE}}_{\kappa }$ at $\kappa =2$.

arXiv comment72 pages, 46 figures; Final version, accepted for publication in Comm. Math. Phys

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Cited by in corpus (6)

• Crossing Probabilities of Multiple Ising Interfaces
• UST branches, martingales, and multiple SLE(2)
• Connection Probabilities of Multiple FK-Ising Interfaces
• Uniform Spanning Tree in Topological Polygons, Partition Functions for SLE(8), and Correlations in $c=-2$ Logarithmic CFT
• Planar UST Branches and $c=-2$ Degenerate Boundary Correlations
• Watermelons on the half-plane