The Covariant Measure of SLE on the Boundary
Probability
2010-03-30 v2
Abstract
We construct a natural measure mu supported on the intersection of a chordal SLE(kappa) curve gamma with the real line R, in the range 4 < kappa < 8. The measure is a function of the SLE path in question. Assuming that boundary measures transform in a ``d-dimensional'' way (where d is the Hausdorff dimension of gamma intersected with R), we show that the measure we construct is (up to multiplicative constant) the unique measure-valued function of the SLE path that satisfies the Domain Markov property.
Cite
@article{arxiv.0810.0940,
title = {The Covariant Measure of SLE on the Boundary},
author = {Tom Alberts and Scott Sheffield},
journal= {arXiv preprint arXiv:0810.0940},
year = {2010}
}
Comments
35 pages; minor corrections to proof of Corollary 5.3