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

Conformal field theory of Gaussian free fields in a multiply connected domain

We implement a version of conformal field theory (CFT) that gives a connection to SLE in a multiply connected domain. Our approach is …

Tom Alberts, Sung-Soo Byun, Nam-Gyu Kang

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

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

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

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

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

Dimension and measure of SLE on the boundary

Tom Alberts

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

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