Coupling and an application to level-set percolation of the Gaussian free field

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Author
Date
2016Type
- Journal Article
Abstract
In the present article we consider a general enough set-up and obtain a refinement of the coupling between the Gaussian free field and random interlacements recently constructed by Titus Lupu in [9]. We apply our results to level-set percolation of the Gaussian free field on a (d+1)-regular tree, when d≥2, and derive bounds on the critical value h∗. In particular, we show that 0<h∗<√2u∗, where u∗ denotes the critical level for the percolation of the vacant set of random interlacements on a (d+1)-regular tree. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000117668Publication status
publishedExternal links
Journal / series
Electronic Journal of ProbabilityVolume
Pages / Article No.
Publisher
Institute of Mathematical StatisticsSubject
Gaussian free field; Random interlacements; Coupling; Level-set percolationOrganisational unit
03320 - Sznitman, Alain-Sol (emeritus) / Sznitman, Alain-Sol (emeritus)
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