SLE

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

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

A dimension spectrum for SLE boundary collisions

We consider chordal SLE

(κ)

κ > 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

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

(κ)

κ < 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

μ

supported on the intersection of a chordal SLE

(κ)

γ

R

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

(κ)

path in the upper half plane

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

(κ)

curve hitting two small intervals on the real line as the …

Tom Alberts, Scott Sheffield