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Level lines of the Gaussian free field with general boundary data

Powell, Ellen; Wu, Hao

Authors

Hao Wu



Abstract

We study the level lines of a Gaussian free field in a planar domain with general boundary data F. We show that the level lines exist as continuous curves under the assumption that F is regulated (i.e., admits finite left and right limits at every point), and satisfies certain inequalities. Moreover, these level lines are a.s. determined by the field. This allows us to define and study a generalization of the SLE4(ρ) process, now with a continuum of force points. A crucial ingredient is a monotonicity property in terms of the boundary data which strengthens a result of Miller and Sheffield and is also of independent interest.

Citation

Powell, E., & Wu, H. (2017). Level lines of the Gaussian free field with general boundary data. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 53(4), 2229-2259. https://doi.org/10.1214/16-aihp789

Journal Article Type Article
Acceptance Date Aug 22, 2016
Publication Date Jan 1, 2017
Deposit Date Sep 28, 2019
Journal Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
Print ISSN 0246-0203
Publisher Institute of Mathematical Statistics
Peer Reviewed Peer Reviewed
Volume 53
Issue 4
Pages 2229-2259
DOI https://doi.org/10.1214/16-aihp789

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