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arXiv · 1710.04261

Multipoint Estimates for Radial and Whole-plane SLE

Benjamin Mackey·Dapeng Zhan
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Abstract

We prove upper bounds for the probability that a radial SLE$_{\kappa}$ curve, $\kappa\in(0,8)$, comes within specified radii of $n$ different points in the unit disc. Using this estimate, we then prove a similar upper bound for a whole-plane SLE$_{\kappa}$ curve. We then use these estimates to show that the lower Minkowski content of both the radial and whole-plane SLE$_{\kappa}$ traces restricted in a bounded region have finite moments of any order.

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Benjamin Mackey, Dapeng Zhan. 2017-10-11. Multipoint Estimates for Radial and Whole-plane SLE. https://arxiv.org/abs/1710.04261

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