On Multiple Schramm-Loewner Evolutions

In this note we consider the ansatz for Multiple Schramm-Loewner Evolutions (SLEs) proposed by Bauer, Bernard and Kytola from a more probabilistic point of view. Here we show their ansatz is a consequence of conformal invariance, reparameterisation invariance and a notion of absolute continuity. In so doing we demonstrate that it is only consistent to grow multiple SLEs if their kappa parameters are related by kappa_i = kappa_j or kappa_i = 16 / kappa_j.

K. Graham · 2005