Critical Ising interfaces in multiply-connected domains

Abstract

We prove a general result on convergence of interfaces in the critical planar Ising model to conformally invariant curves absolutely continuous with respect to SLE(3). Our setup includes multiple interfaces on arbitrary finitely connected domains, and we also treat the radial SLE case. In the case of simply and doubly connected domains, the limiting processes are described explicitly in terms of rational and elliptic functions, respectively.

arXiv comment31 pages. Presentation rearranged, with more discussion of SLE partition functions in the introduction, and some parts rewritten. Part of my Ph. D. thesis