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arXiv · 1506.04679

Multiple SLE and the complex Burgers equation

Andrea del Monaco·Sebastian Schleissinger
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Abstract

In this paper we ask whether one can take the limit of multiple SLE as the number of slits goes to infinity. In the special case of $n$ slits that connect $n$ points of the boundary to one fixed point, one can take the limit of the Loewner equation that describes the growth of those slits in a simultaneous way. In this case, the limit is a deterministic Loewner equation whose vector field is determined by a complex Burgers equation.

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Andrea del Monaco, Sebastian Schleissinger. 2015-06-15. Multiple SLE and the complex Burgers equation. https://arxiv.org/abs/1506.04679

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