On Multiple Schramm-Loewner Evolutions

Abstract

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.

21 pages, 4 figures

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• Multiple backward Schramm--Loewner evolution and coupling with Gaussian free field
• Limits of radial multiple SLE and a Burgers-Loewner differential equation
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