SLE-type growth processes and the Yang-Lee singularity

Lesage, Frédéric and Rasmussen, Jørgen (2004) SLE-type growth processes and the Yang-Lee singularity. Journal of Mathematical Physics, 45 8: 3040-3048. doi:10.1063/1.1765747

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Author Lesage, Frédéric
Rasmussen, Jørgen
Title SLE-type growth processes and the Yang-Lee singularity
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
Publication date 2004-08-01
Year available 2004
Sub-type Article (original research)
DOI 10.1063/1.1765747
Open Access Status File (Publisher version)
Volume 45
Issue 8
Start page 3040
End page 3048
Total pages 9
Place of publication College Park, MD, United States
Publisher American Institute of Physics
Language eng
Formatted abstract
The recently introduced SLE growth processes are based on conformal maps from an open and simply connected subset of the upper half-plane to the half-plane itself. We generalize this by considering a hierarchy of stochastic evolutions mapping open and simply connected subsets of smaller and smaller fractions of the upper half-plane to these fractions themselves. The evolutions are all driven by one-dimensional Brownian motion. Ordinary chordal SLE appears at grade one in the hierarchy. At grade two we find a direct correspondence to conformal field theory through the explicit construction of a level-four null vector in a highest-weight module of the Virasoro algebra. This conformal field theory has central charge c = - 22/5 and is associated with the Yang-Lee singularity. Our construction may thus offer a novel description of this statistical model.
Keyword Physics, Mathematical
Physics
PHYSICS, MATHEMATICAL
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Citation counts: TR Web of Science Citation Count  Cited 4 times in Thomson Reuters Web of Science Article | Citations
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Created: Wed, 21 Mar 2012, 23:03:36 EST by Kay Mackie on behalf of Mathematics