Boundary Correlations in Planar LERW and UST

Alex Karrila; Kalle Kytölä; Eveliina Peltola

doi:10.1007/s00220-019-03615-0

Boundary Correlations in Planar LERW and UST

Alex Karrila
, Kalle Kytölä
, Eveliina Peltola^*

^*Corresponding author for this work

University of Geneva

Research output: Contribution to journal › Article › Scientific › peer-review

15 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 language	English
Pages (from-to)	2065–2145
Number of pages	81
Journal	Communications in Mathematical Physics
Volume	376
Early online date	1 Jan 2019
DOIs	https://doi.org/10.1007/s00220-019-03615-0
Publication status	Published - 2020
MoE publication type	A1 Journal article-refereed

Funding

We thank Christian Hagendorf for useful discussions, and in particular for drawing our attention to the results of [ KW11a , KW11b , KW15 ]. We also thank Dmitry Chelkak, Steven Flores, Christophe Garban, Konstantin Izyurov, Richard Kenyon, Marcin Lis, Wei Qian, David Radnell, Fredrik Viklund, David Wilson, and Hao Wu for interesting and helpful discussions. A.K. and K.K. are supported by the Academy of Finland project “Algebraic structures and random geometry of stochastic lattice models”. During this work, E.P. was supported by Vilho, Yrjö and Kalle Väisälä Foundation and later by the ERC AG COMPASP, the NCCR SwissMAP, and the Swiss NSF.

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10.1007/s00220-019-03615-0

https://arxiv.org/pdf/1702.03261

Cite this

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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.",

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AB - 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.

UR - https://www.scopus.com/pages/publications/85075345206

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Boundary Correlations in Planar LERW and UST

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