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Published December 14, 2012 | public
Journal Article

The Green function for the radial Schramm–Loewner evolution

Abstract

We prove the existence of the Green function for radial SLE_κ for κ < 8. Unlike the chordal case where an explicit formula for the Green function is known for all values of κ < 8, we give an explicit formula only for κ = 4. For other values of κ, we give a formula in terms of an expectation with respect to SLE conditioned to go through a point.

Additional Information

© 2012 Institute of Physics. Received 16 July 2012, in final form 5 October 2012. Published 27 November 2012. This article is part of 'Lattice models and integrability', a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday. This paper had its origin at the Random Spatial Processes program held at the Mathematical Sciences Research Institute in Berkeley, CA, during spring 2012. All three authors benefitted from extended visits to MSRI and are grateful to the organizers for the invitation to participate in the program. Thanks are also owed to Dapeng Zhan, Nikolai Makarov and Nam-Gyu Kang for useful discussions. The research of the second author is supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the research of the third author is supported by National Science Foundation grant DMS-0907143.

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023