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Configurations of FK Ising interfaces and hypergeometric SLE

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arxiv 1704.02823 v1 pith:NFWAEMDQ submitted 2017-04-10 math-ph math.MPmath.PR

Antti Kemppainen , Stanislav Smirnov This is my paper · ORCID
classification math-phmath.MPmath.PR
keywords interfaceshsleboundaryconfigurationdomainhypergeometricisinglimit
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In this paper, we show that the interfaces in FK Ising model in any domain with 4 marked boundary points and wired--free--wired--free boundary conditions conditioned on a specific internal arc configuration of interfaces converge in the scaling limit to hypergeometric SLE (hSLE). The arc configuration consists of a pair of interfaces and the scaling limit of their joint law can be described by an algorithm to sample the pair from a hSLE curve and a chordal SLE (in a random domain defined by the hSLE).

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  1. Connection probabilities in the double-dimer model -- the case of two connectivity patterns

    math-ph 2019-08 conditional novelty 5.0 of 10

    Using Grassmannian integrals, the double-dimer connection probability on a rectangle is shown to converge in the continuum to the known SLE4/CLE4 value (1-x)/(1+x).

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