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dc.contributor.author
Abächerli, Angelo
dc.contributor.author
Černý, Jiří
dc.date.accessioned
2021-08-02T19:23:31Z
dc.date.available
2020-11-11T06:13:09Z
dc.date.available
2020-11-13T08:39:46Z
dc.date.available
2021-08-02T13:52:14Z
dc.date.available
2021-08-02T19:23:31Z
dc.date.issued
2020
dc.identifier.issn
1083-6489
dc.identifier.other
10.1214/20-EJP532
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/450689
dc.identifier.doi
10.3929/ethz-b-000450689
dc.description.abstract
We consider the zero-average Gaussian free field on a certain class of finite d-regular graphs for fixed d >= 3. This class includes d-regular expanders of large girth and typical realisations of random d-regular graphs. We show that the level set of the zero-average Gaussian free field above level h(*), exhibits a phase transition at level which agrees with the critical value for level-set percolation of the Gaussian free field on the infinite d-regular tree. More precisely, we show that, with probability tending to one as the size of the finite graphs tends to infinity, the level set above level h does not contain any connected component of larger than logarithmic size whenever h > h(*), and on the contrary, whenever h < h(*), linear fraction of the vertices is contained in connected components of the level set above level h having a size of at least a small fractional power of the total size of the graph. It remains open whether in the supercritical phase h < h(*), as the size of the graphs tends to infinity, one observes the emergence of a (potentially unique) giant connected component of the level set above level h. The proofs in this article make use of results from the accompanying paper [2].
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Institute of Mathematical Statistics
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 graphs
en_US
dc.subject
expander graphs
en_US
dc.title
Level-set percolation of the Gaussian free field on regular graphs II: finite expanders
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
ethz.journal.title
Electronic Journal of Probability
ethz.journal.volume
25
en_US
ethz.journal.abbreviated
Electron. J. Probab.
ethz.pages.start
130
en_US
ethz.size
40 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.publication.place
Beachwood, OH
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)
en_US
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
2020-11-11T06:13:19Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2020-11-13T08:39:59Z
ethz.rosetta.lastUpdated
2021-02-15T20:44:42Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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