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dc.contributor.author
Nitzschner, Maximilian
dc.date.accessioned
2021-08-02T14:11:56Z
dc.date.available
2019-01-14T08:53:11Z
dc.date.available
2021-08-02T13:48:55Z
dc.date.available
2021-08-02T14:11:56Z
dc.date.issued
2018-10-23
dc.identifier.issn
1083-6489
dc.identifier.other
10.1214/18-EJP226
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/315429
dc.identifier.doi
10.3929/ethz-b-000315429
dc.description.abstract
We derive asymptotic upper and lower bounds on the large deviation probability that the level set of the Gaussian free field on Zd, d≥3, below a level α, disconnects the discrete blow-up of a compact set A from the boundary of the discrete blow-up of a box that contains A, when the level set of the Gaussian free field above α is in a strongly percolative regime. These bounds substantially strengthen the results of [21], where A was a box and the convexity of A played an important role in the proof. We also derive an asymptotic upper bound on the probability that the average of the Gaussian free field well inside the discrete blow-up of A is above a certain level when disconnection occurs. The derivation of the upper bounds uses the solidification estimates for porous interfaces that were derived in the work [15] of A.-S. Sznitman and the author to treat a similar disconnection problem for the vacant set of random interlacements. If certain critical levels for the Gaussian free field coincide, an open question at the moment, the asymptotic upper and lower bounds that we obtain for the disconnection probability match in principal order, and conditioning on disconnection lowers the average of the Gaussian free field well inside the discrete blow-up of A, which can be understood as entropic repulsion.
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
Gaussian free field
en_US
dc.subject
Disconnection
en_US
dc.subject
Level-set percolation
en_US
dc.subject
Entropic repulsion
en_US
dc.title
Disconnection by level sets of the discrete Gaussian free field and entropic repulsion
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
23
en_US
ethz.journal.abbreviated
Electron. J. Probab.
ethz.pages.start
105
en_US
ethz.size
21 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
2018-11-09T04:44:42Z
ethz.source
BATCH
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2020-02-24T08:23:50Z
ethz.rosetta.lastUpdated
2022-03-29T10:52:49Z
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/313443
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/302082
ethz.COinS
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