Multi-point Green's functions for SLE and an estimate of Beffara
| Autor: | Lawler, Gregory F., Werness, Brent M. |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Annals of Probability 2013, Vol. 41, No. 3A, 1513-1555 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1214/11-AOP695 |
| Popis: | In this paper we define and prove of the existence of the multi-point Green's function for SLE - a normalized limit of the probability that an $SLE_{\kappa}$ curve passes near to 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 to our proof is a refinement of a bound first provided by Beffara [Ann. Probab. 36 (2008) 1421-1452]. This work contains a proof of this bound independent from the original. Comment: Published in at http://dx.doi.org/10.1214/11-AOP695 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | arXiv |
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