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Multi-point Green’s functions for SLE and an estimate of Beffara. (English) Zbl 1277.60134
Summary: We define and prove of the existence of the multi-point Green function for Schramm-Loewner evolution (SLE) – a normalized limit of the probability that an SLE\(_{\kappa}\)-curve passes near a pair of marked points in the interior of a domain. When \(\kappa<8\), this probability is nontrivial, and an expression can be written in terms two-sided radial SLE. One of the main components of our proof is a refinement of a bound first provided by V. Beffara [Ann. Probab. 36, No. 4, 1421–1452 (2008; Zbl 1165.60007)]. This work contains a proof of this bound independent from the original.

60J67 Stochastic (Schramm-)Loewner evolution (SLE)
82B27 Critical phenomena in equilibrium statistical mechanics
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