# Basic properties of SLE

### Abstract

$\mathrm{SLE}_{\kappa}$ is a random growth process based on Loewner’s equation with driving parameter a one-dimensional Brownian motion running with speed $\kappa$. This process is intimately connected with scaling limits of percolation clusters and with the outer boundary of Brownian motion, and is conjectured to correspond to scaling limits of several other discrete processes in two dimensions.

## Authors

Steffen Rohde

Department of Mathematics, University of Washington, Seattle, WA 98195, United States

Oded Schramm

Microsoft Research Corporation, Redmond, WA 98052, United States