Level lines of the Gaussian free field with general boundary data
Accepted version
Peer-reviewed
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Repository DOI
Change log
Authors
Powell, EG
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.
Description
Keywords
Gaussian free field, Level lines, Schramm Loewner evolution
Journal Title
Annales de l'institut Henri Poincare (B) Probability and Statistics
Conference Name
Journal ISSN
0246-0203
Volume Title
Publisher
Elsevier