Boundary Correlations in Planar LERW and UST

Alex Karrila, Kalle Kytölä, Eveliina Peltola*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

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 SLE κ at κ= 2.

Original languageEnglish
JournalCOMMUNICATIONS IN MATHEMATICAL PHYSICS
DOIs
Publication statusE-pub ahead of print - 1 Jan 2019
MoE publication typeA1 Journal article-refereed

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