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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2005

Dipolar SLEs

M. Bauer
Denis Bernard
J. Houdayer

Résumé

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.

Dates et versions

hal-00021801 , version 1 (26-03-2006)

Identifiants

Citer

M. Bauer, Denis Bernard, J. Houdayer. Dipolar SLEs. Journal of Statistical Mechanics: Theory and Experiment, 2005, 0503, pp.P001. ⟨10.1088/1742-5468/2005/03/P03001⟩. ⟨hal-00021801⟩
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