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arXiv · 1702.03261

Boundary correlations in planar LERW and UST

Alex Karrila·Kalle Kytölä·Eveliina Peltola
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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 $\mathrm{SLE}_\kappa$ at $\kappa=2$.

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Alex Karrila, Kalle Kytölä, Eveliina Peltola. 2017-02-10. Boundary correlations in planar LERW and UST. https://doi.org/10.1007/s00220-019-03615-0

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