The configurational measure on mutually avoiding SLE paths

By Michael J. Kozdron, Gregory F. Lawler. 2006

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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 lambda-SAW, a one-parameter family of measures on self-avoiding walks on Z^2.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dce7e34177db5d6df97e002d95758d41533f015c