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dc.contributor.author
Windisch, David
dc.date.accessioned
2021-07-30T11:55:30Z
dc.date.available
2021-07-30T11:55:30Z
dc.date.issued
2008
dc.identifier.issn
1083-6489
dc.identifier.other
10.1214/EJP.v13-506
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/498674
dc.identifier.doi
10.3929/ethz-b-000004514
dc.description.abstract
This work continues the investigation, initiated in a recent work by Benjamini and Sznitman, of percolative properties of the set of points not visited by a random walk on the discrete torus (Z/NZ)d up to time uNd in high dimension d. If u>0 is chosen sufficiently small it has been shown that with overwhelming probability this vacant set contains a unique giant component containing segments of length c0logN for some constant c0>0, and this component occupies a non-degenerate fraction of the total volume as N tends to infinity. Within the same setup, we investigate here the complement of the giant component in the vacant set and show that some components consist of segments of logarithmic size. In particular, this shows that the choice of a sufficiently large constant c0>0 is crucial in the definition of the giant component.
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/3.0/
dc.subject
Gaint component
en_US
dc.subject
vacant set
en_US
dc.subject
random walk
en_US
dc.subject
discrete torus
en_US
dc.title
Logarithmic Components of the Vacant Set for Random Walk on a Discrete Torus
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 3.0 Unported
dc.date.published
2016-06-01
ethz.journal.title
Electronic Journal of Probability
ethz.journal.volume
13
en_US
ethz.journal.abbreviated
Electron. J. Probab.
ethz.pages.start
880
en_US
ethz.pages.end
897
en_US
ethz.size
18 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.identifier.scopus
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)
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
2017-06-08T16:39:14Z
ethz.source
ECIT
ethz.identifier.importid
imp59364b7b28d9915497
ethz.identifier.importid
imp59364bf4a7cc457444
ethz.ecitpid
pub:14660
ethz.ecitpid
pub:21703
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2021-07-30T11:55:38Z
ethz.rosetta.lastUpdated
2022-03-29T10:50:18Z
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/4514
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/161888
ethz.COinS
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