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Multipoint Estimates for Radial and Whole-Plane SLE

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Abstract

We prove upper bounds for the probability that a radial \(\hbox {SLE}_{\kappa }\) 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 \(\hbox {SLE}_{\kappa }\) curve. We then use these estimates to show that the lower Minkowski content of both the radial and whole-plane \(\hbox {SLE}_{\kappa }\) traces restricted in a bounded region have finite moments of any order.

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Authors and Affiliations

  1. The University of Akron, Akron, USA

    Benjamin Mackey

  2. Michigan State University, East Lansing, USA

    Dapeng Zhan

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  1. Benjamin Mackey
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  2. Dapeng Zhan
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Correspondence to Dapeng Zhan.

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Communicated by Eric Carlen.

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Dapeng Zhan: Partially supported by NSF Grant DMS-1056840 and Simons Foundation Grant #396973.

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Mackey, B., Zhan, D. Multipoint Estimates for Radial and Whole-Plane SLE. J Stat Phys 175, 879–903 (2019). https://doi.org/10.1007/s10955-019-02269-5

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  • DOI: https://doi.org/10.1007/s10955-019-02269-5

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