Affordable Access

The configurational measure on mutually avoiding SLE paths

Authors
  • Kozdron, Michael J.
  • Lawler, Gregory F.
Type
Published Article
Publication Date
Jun 07, 2006
Submission Date
May 07, 2006
Identifiers
arXiv ID: math/0605159
Source
arXiv
License
Unknown
External links

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

Report this publication

Statistics

Seen <100 times