Coupling the Gaussian Free Fields with Free and with Zero Boundary Conditions via Common Level Lines
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Authors
Qian, W
Werner, Wendelin
Publication Date
2018-07-01Journal Title
Communications in Mathematical Physics
ISSN
1432-0916
Publisher
Springer Nature
Volume
361
Issue
1
Pages
53-80
Language
eng
Type
Article
This Version
VoR
Metadata
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Qian, W., & Werner, W. (2018). Coupling the Gaussian Free Fields with Free and with Zero Boundary Conditions via Common Level Lines. Communications in Mathematical Physics, 361 (1), 53-80. https://doi.org/10.1007/s00220-018-3159-z
Abstract
We point out a new simple way to couple the Gaussian free field (GFF) with free boundary conditions in a two-dimensional domain with the GFF with zero boundary conditions in the same domain: Starting from the latter, one just has to sample at random all the signs of the height gaps on its boundary-touching zero level lines (these signs are alternating for the zero-boundary GFF) in order to obtain a free boundary GFF. Constructions and couplings of the free boundary GFF and its level lines via soups of reflected Brownian loops and their clusters are also discussed. Such considerations show for instance that in a domain with an axis of symmetry, if one looks at the overlay of a single usual Conformal Loop Ensemble CLE3 with its own symmetric image, one obtains the CLE4-type collection of level lines of a GFF with mixed zero/free boundary conditions in the half-domain.
Sponsorship
We acknowledge support of the Grant No. 155922 (WQ, WW) and an Early Postdoc.Mobility Grant (WQ) of the SNF. The authors are/were part of NCCR SwissMAP
Identifiers
External DOI: https://doi.org/10.1007/s00220-018-3159-z
This record's URL: https://www.repository.cam.ac.uk/handle/1810/278794
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