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SLE
Pole dynamics and an integral of motion for multiple SLE(0)
We describe the Loewner chains of the real locus of a class of real rational functions whose critical points are on the real line. Our …
Tom Alberts
,
Nam-Gyu Kang
,
Nikolai Makarov
,
Sung-Soo Byun
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A dimension spectrum for SLE boundary collisions
We consider chordal SLE$(\kappa)$ curves for $\kappa > 4$, where the intersection of the curve with the boundary is a random fractal …
Tom Alberts
,
Ilia Binder
,
Fredrik Viklund
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DOI
Some partial results on the convergence of loop-erased random walk to SLE(2) in the natural parametrization
We outline a strategy for showing convergence of loop-erased random walk on the $\mathbb{Z}^2$ square lattice to SLE(2), in the …
Tom Alberts
,
Michael Kozdron
,
Robert Masson
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The Green function for the radial Schramm-Loewner evolution
We prove the existence of the Green function for radial SLE$(\kappa)$ for $\kappa < 8$. Unlike the chordal case where an explicit …
Tom Alberts
,
Michael Kozdron
,
Gregory Lawler
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The covariant measure of SLE on the boundary
We construct a natural measure $\mu$ supported on the intersection of a chordal SLE$(\kappa)$ curve $\gamma$ with $\mathbb{R}$, in the …
Tom Alberts
,
Scott Sheffield
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Bridge decomposition of restriction measures
Motivated by Kesten’s bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the …
Tom Alberts
,
Hugo Duminil-Copin
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Dimension and measure of SLE on the boundary
Tom Alberts
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Intersection probabilities for a chordal SLE path and a semicircle
We derive a number of estimates for the probability that a chordal SLE$(\kappa)$ path in the upper half plane $\mathbb{H}$ intersects a …
Tom Alberts
,
Michael Kozdron
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Hausdorff dimension of the SLE curve intersected with the real line
We establish an upper bound on the asymptotic probability of an SLE$(\kappa)$ curve hitting two small intervals on the real line as the …
Tom Alberts
,
Scott Sheffield
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