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Multiple-paths $SLE_\kappa$ in multiply connected domains

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arxiv 1811.05066 v1 pith:3WPVTLHO submitted 2018-11-13 math.PR

Mohammad Jahangoshahi , Gregory F. Lawler This is my paper
classification math.PR
keywords kappaconnecteddomainsfunctionmeasuremultiple-pathsmultiplypartition
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abstract

We define multiple-paths Schramm-Loewner evolution ($SLE_\kappa$) in multiply connected domains when $\kappa\leq 4$ and prove that in annuli, the partition function is smooth. Moreover, we give up-to-constant estimates for the partition function of bi-chordal annulus $SLE_\kappa$ measure and we establish a connection between this measure and two-sided $SLE_\kappa$ in the unit disk.

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    Explicit theta-function formulas give the probability that all GFF level lines cross an annulus, with a new sqrt(r) correction as the inner hole shrinks.

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