Slit Holomorphic Stochastic Flows and Gaussian Free Field

It was realized recently that the chordal, radial and dipolar Schramm–Löwner evolution (SLEs) are special cases of a general slit holomorphic stochastic flow. We characterize those slit holomorphic stochastic flows which generate level lines of the Gaussian free field. In particular, we describe the...

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Bibliographic Details
Published inComplex analysis and operator theory Vol. 10; no. 7; pp. 1591 - 1617
Main Authors Ivanov, Georgy, Kang, Nam-Gyu, Vasil’ev, Alexander
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2016
Springer Nature B.V
Subjects
Analysis
Boundary conditions
Mathematics
Mathematics and Statistics
Operator Theory
60D05
Gaussian free field
Slit holomorphic stochastic flows
34M99
SLE
30C35
60J67
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Summary:It was realized recently that the chordal, radial and dipolar Schramm–Löwner evolution (SLEs) are special cases of a general slit holomorphic stochastic flow. We characterize those slit holomorphic stochastic flows which generate level lines of the Gaussian free field. In particular, we describe the modifications of the Gaussian free field (GFF) corresponding to the chordal and dipolar SLE with drifts. Finally, we develop a version of conformal field theory based on the background charge and Dirichlet boundary condition modifications of GFF and present martingale-observables for these types of SLEs.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-016-0536-5