Show simple item record

dc.contributor.author
Lemm, Marius
dc.contributor.author
Sutter, David
dc.date.accessioned
2020-10-30T07:42:06Z
dc.date.available
2020-10-21T12:03:11Z
dc.date.available
2020-10-23T08:10:13Z
dc.date.available
2020-10-30T07:42:06Z
dc.date.issued
2020
dc.identifier.uri
http://hdl.handle.net/20.500.11850/447035
dc.description.abstract
The Lyapunov exponent characterizes the asymptotic behavior of long matrix products. Recognizing scenarios where the Lyapunov exponent is strictly positive is a fundamental challenge that is relevant in many applications. In this work we establish a novel tool for this task by deriving a quantitative lower bound on the Lyapunov exponent in terms of a matrix sum which is efficiently computable in ergodic situations. Our approach combines two deep results from matrix analysis --- the n-matrix extension of the Golden-Thompson inequality and the Avalanche-Principle. We apply these bounds to the Lyapunov exponents of Schrödinger cocycles with certain ergodic potentials of polymer type and arbitrary correlation structure. We also derive related quantitative stability results for the Lyapunov exponent near aligned diagonal matrices and a bound for almost-commuting matrices.
en_US
dc.language.iso
en
en_US
dc.publisher
Cornell University
en_US
dc.title
Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities
en_US
dc.type
Working Paper
dc.date.published
2020-01-24
ethz.journal.title
arXiv
ethz.pages.start
2001.09115
en_US
ethz.size
46 p.
en_US
ethz.identifier.arxiv
2001.09115
ethz.publication.place
Ithaca, NY
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03781 - Renner, Renato / Renner, Renato
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03781 - Renner, Renato / Renner, Renato
ethz.relation.isPreviousVersionOf
handle/20.500.11850/527064
ethz.date.deposited
2020-10-21T12:03:21Z
ethz.source
BATCH
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-10-23T08:10:24Z
ethz.rosetta.lastUpdated
2021-02-15T19:28:57Z
ethz.rosetta.versionExported
true
ethz.COinS
ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.atitle=Quantitative%20lower%20bounds%20on%20the%20Lyapunov%20exponent%20from%20multivariate%20matrix%20inequalities&rft.jtitle=arXiv&rft.date=2020&rft.spage=2001.09115&rft.au=Lemm,%20Marius&Sutter,%20David&rft.genre=preprint&
 Search print copy at ETH Library

Files in this item

FilesSizeFormatOpen in viewer

There are no files associated with this item.

Publication type

Show simple item record