Schramm–Loewner evolution

Summary

The Schramm–Loewner evolution with parameter $\kappa > 0$, written $\mathrm{SLE}_\kappa$, is a random curve in a planar domain. It is obtained from the Loewner differential equation driven by a multiple of a Brownian motion. Oded Schramm introduced it in 2000 as the candidate scaling limit of interfaces in planar models of statistical physics that are conformally invariant. It is characterised by conformal invariance together with a domain Markov property, and the single parameter $\kappa$ governs the shape of the curve.