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The Green function for the radial Schramm–Loewner evolution

Alberts, Tom and Kozdron, Michael J. and Fawler, Gregory F. (2012) The Green function for the radial Schramm–Loewner evolution. Journal of Physics A: Mathematical and Theoretical, 45 (49). Art. No. 494015. ISSN 1751-8113. doi:10.1088/1751-8113/45/49/494015. https://resolver.caltech.edu/CaltechAUTHORS:20130115-111632343

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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.


Item Type:Article
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http://dx.doi.org/10.1088/1751-8113/45/49/494015DOIUNSPECIFIED
http://iopscience.iop.org/1751-8121/45/49/494015/PublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council (NSERC) of CanadaUNSPECIFIED
NSFDMS-0907143
Issue or Number:49
Classification Code:PACS: 02.50.Fz, 05.10.Gg, 02.30.Jr. MSC:34B27, 60J65, 82B21
DOI:10.1088/1751-8113/45/49/494015
Record Number:CaltechAUTHORS:20130115-111632343
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130115-111632343
Official Citation:The Green function for the radial Schramm–Loewner evolution Tom Alberts et al 2012 J. Phys. A: Math. Theor. 45 494015
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36390
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:15 Jan 2013 21:07
Last Modified:09 Nov 2021 23:21

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