The configurational measure on mutually avoiding SLE paths

Abstract

We define multiple chordal SLEs in a simply connected domain by considering a natural configurational measure on paths.We show how to construct these measures so that they are conformally covariant and satisfy certain boundary perturbation and Markov properties, as well as a cascade relation.As an example of our construction, we derive the scaling limit of Fomin's identity in the case of two paths directly; that is, we prove that the probability that an SLE 2 and a Brownian excursion do not intersect can be given in terms of the determinant of the excursion hitting matrix.Finally, we define the λ-SAW, a one-parameter family of measures on self-avoiding walks on Z 2 .