Multipoint Estimates for Radial and Whole-Plane SLE

Multipoint Estimates for Radial and Whole-Plane SLE

We prove upper bounds for the probability that a radial SLE κ curve, κ ∈ ( 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 κ curve. We then use these estimates to show that the lower Minkows...

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Veröffentlicht in:Journal of statistical physics 2019-06, Vol.175 (5), p.879-903
Hauptverfasser: Mackey, Benjamin, Zhan, Dapeng
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Upper bounds
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Zusammenfassung:We prove upper bounds for the probability that a radial SLE κ curve, κ ∈ ( 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 κ curve. We then use these estimates to show that the lower Minkowski content of both the radial and whole-plane SLE κ traces restricted in a bounded region have finite moments of any order.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-019-02269-5