Slit holomorphic stochastic flows and Gaussian free field
Probability
2015-08-14 v1 Mathematical Physics
Complex Variables
math.MP
Abstract
It was realized recently that the chordal, radial and dipolar SLEs are special cases of a general slit holomorphic stochastic flow. We characterize those slit holomorphic stochastic flows which generate level lines of the Gaussian free field. In particular, we describe the modifications of the Gaussian free field (GFF) corresponding to the chordal and dipolar SLE with drifts. Finally, we develop a version of conformal field theory based on the background charge and Dirichlet boundary condition modifications of GFF and present martingale-observables for these types of SLEs.
Keywords
Cite
@article{arxiv.1508.03160,
title = {Slit holomorphic stochastic flows and Gaussian free field},
author = {Georgy Ivanov and Nam-Gyu Kang and Alexander Vasil'ev},
journal= {arXiv preprint arXiv:1508.03160},
year = {2015}
}