SLE

A Gentle Introduction to Kang-Makarov Conformal Field Theory

A simplified introduction to the conformal field theory of Kang and Makarov.

May 25, 2022 08:00 -0900 — 09:00 -0900 Mathematical Sciences Research Institute

Tom Alberts

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