Dipolar SLEs
摘要
We present basic properties of Dipolar SLEs, a new version of stochastic Loewner evolutions (SLE) in which the critical interfaces end randomly on an interval of the boundary of a planar domain. We present a general argument explaining why correlation functions of models of statistical mechanics are expected to be martingales and we give a relation between dipolar SLEs and CFTs. We compute SLE excursion and/or visiting probabilities, including the probability for a point to be on the left/right of the SLE trace or that to be inside the SLE hull. These functions, which turn out to be harmonic, have a simple CFT interpretation. We also present numerical simulations of the ferromagnetic Ising interface that confirm both the probabilistic approach and the CFT mapping.
引用
@article{arxiv.math-ph/0411038,
title = {Dipolar SLEs},
author = {M. Bauer and D. Bernard and J. Houdayer},
journal= {arXiv preprint arXiv:math-ph/0411038},
year = {2011}
}
备注
22 pages, 4 figures