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dc.contributor.author
Abaecherli, Angelo
dc.contributor.author
Černý, Jiří
dc.date.accessioned
2020-07-10T07:15:17Z
dc.date.available
2020-07-03T19:08:43Z
dc.date.available
2020-07-10T07:15:17Z
dc.date.issued
2020
dc.identifier.issn
1083-6489
dc.identifier.other
10.1214/20-EJP468
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/424327
dc.identifier.doi
10.3929/ethz-b-000424327
dc.description.abstract
We study level-set percolation of the Gaussian free field on the infinite d-regular tree for fixed d >= 3. Denoting by h(*) the critical value, we obtain the following results: for h > h(*) we derive estimates on conditional exponential moments of the size of a fixed connected component of the level set above level h; for h < h(*) we prove that the number of vertices connected over distance k above level h to a fixed vertex grows exponentially in k with positive probability. Furthermore, we show that the percolation probability is a continuous function of the level h, at least away from the critical value h(*). Along the way we also obtain matching upper and lower bounds on the eigenfunctions involved in the spectral characterisation of the critical value h(*) and link the probability of a non-vanishing limit of the martingale used therein to the percolation probability. A number of the results derived here are applied in the accompanying paper [1].
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
University of Washington, Mathematics Departement
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Level-set percolation
en_US
dc.subject
Gaussian free field
en_US
dc.subject
regular tree
en_US
dc.title
Level-set percolation of the Gaussian free field on regular graphs I: regular trees
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2020-06-18
ethz.journal.title
Electronic Journal of Probability
ethz.journal.volume
25
en_US
ethz.journal.abbreviated
Electron. J. Probab.
ethz.pages.start
65
en_US
ethz.size
24 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.publication.place
Seattle, WA
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03320 - Sznitman, Alain-Sol (emeritus) / Sznitman, Alain-Sol (emeritus)
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03320 - Sznitman, Alain-Sol (emeritus) / Sznitman, Alain-Sol (emeritus)
ethz.date.deposited
2020-07-03T19:08:48Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2020-07-10T07:15:28Z
ethz.rosetta.lastUpdated
2021-02-15T15:23:56Z
ethz.rosetta.versionExported
true
ethz.COinS
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