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dc.contributor.author
Mathieu, Pierre
dc.contributor.author
Sisto, Alessandro
dc.date.accessioned
2017-06-11T15:02:16Z
dc.date.available
2017-06-11T15:02:16Z
dc.date.issued
2014-11-28
dc.identifier.uri
http://hdl.handle.net/20.500.11850/95260
dc.description.abstract
We study random walks on groups with the feature that, roughly speaking, successive positions of the walk tend to be "aligned". We formalize and quantify this property by means of the notion of deviation inequalities. On one hand, we show that the (exponential) deviation inequality holds for measures with exponential tail on what we call acylindrically hyperbolic groups with hierarchy paths. These include non-elementary (relatively) hyperbolic groups, Mapping Class Groups, groups acting on CAT(0) cube complexes and small cancellation groups. On the other hand, we show that deviation inequalities have several consequences including the local Lipschitz continuity of the rate of escape and entropy, as well as linear upper and lower bounds on the variance of the distance of the position of the walk from its initial point.
dc.language.iso
en
dc.publisher
Cornell University
dc.subject
Random walks
dc.subject
Rate of escape
dc.subject
Entropy
dc.subject
Girsanov
dc.subject
Hyperbolic groups
dc.title
Deviation inequalities for random walks
dc.type
Working Paper
ethz.journal.title
arXiv
ethz.pages.start
arXiv:1411.7865
ethz.notes
.
ethz.publication.place
Ithaca, NY
ethz.publication.status
published
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::09561 - Sisto, Alessandro / Sisto, Alessandro
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::08802 - Iozzi, Alessandra (Tit.-Prof.)
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::09561 - Sisto, Alessandro / Sisto, Alessandro
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::08802 - Iozzi, Alessandra (Tit.-Prof.)
ethz.identifier.url
http://arxiv.org/abs/1411.7865
ethz.date.deposited
2017-06-11T15:02:54Z
ethz.source
ECIT
ethz.identifier.importid
imp593652bba3b5379942
ethz.ecitpid
pub:149453
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-13T18:16:01Z
ethz.rosetta.lastUpdated
2018-11-02T17:30:06Z
ethz.rosetta.versionExported
true
ethz.COinS
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