Dipolar SLEs

Details Dipolar SLEs Dipolar SLEs

2004-11-10

arxiv.org/abs/math-ph/0411038v1

J.Stat.Mech.0503:P03001,2005

Physics

Mathematical Physics

22 pages, 4 figures

Scientific paper

10.1088/1742-5468/2005/03/P03001

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.

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