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Article: Dobrushin’s Ergodicity Coefficient for Markov Operators on Cones
Title | Dobrushin’s Ergodicity Coefficient for Markov Operators on Cones |
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Authors | |
Keywords | ordered linear space zero error capacity rank one matrix noncommutative Markov chain Markov operator invariant measure Dobrushin’s ergodicity coefficient contraction ratio consensus quantum channel |
Issue Date | 2014 |
Citation | Integral Equations and Operator Theory, 2014, v. 81, n. 1, p. 127-150 How to Cite? |
Abstract | © 2014, Springer Basel. Doeblin and Dobrushin characterized the contraction rate of Markov operators with respect the total variation norm. We generalize their results by giving an explicit formula for the contraction rate of a Markov operator over a cone in terms of pairs of extreme points with disjoint support in a set of abstract probability measures. By duality, we derive a characterization of the contraction rate of consensus dynamics over a cone with respect to Hopf’s oscillation seminorm (the infinitesimal seminorm associated with Hilbert’s projective metric). We apply these results to Kraus maps (noncommutative Markov chains, representing quantum channels), and characterize the ultimate contraction of the map in terms of the existence of a rank one matrix in a certain subspace. |
Persistent Identifier | http://hdl.handle.net/10722/219773 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 0.654 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Gaubert, Stéphane | - |
dc.contributor.author | Qu, Zheng | - |
dc.date.accessioned | 2015-09-23T02:57:55Z | - |
dc.date.available | 2015-09-23T02:57:55Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Integral Equations and Operator Theory, 2014, v. 81, n. 1, p. 127-150 | - |
dc.identifier.issn | 0378-620X | - |
dc.identifier.uri | http://hdl.handle.net/10722/219773 | - |
dc.description.abstract | © 2014, Springer Basel. Doeblin and Dobrushin characterized the contraction rate of Markov operators with respect the total variation norm. We generalize their results by giving an explicit formula for the contraction rate of a Markov operator over a cone in terms of pairs of extreme points with disjoint support in a set of abstract probability measures. By duality, we derive a characterization of the contraction rate of consensus dynamics over a cone with respect to Hopf’s oscillation seminorm (the infinitesimal seminorm associated with Hilbert’s projective metric). We apply these results to Kraus maps (noncommutative Markov chains, representing quantum channels), and characterize the ultimate contraction of the map in terms of the existence of a rank one matrix in a certain subspace. | - |
dc.language | eng | - |
dc.relation.ispartof | Integral Equations and Operator Theory | - |
dc.subject | ordered linear space | - |
dc.subject | zero error capacity | - |
dc.subject | rank one matrix | - |
dc.subject | noncommutative Markov chain | - |
dc.subject | Markov operator | - |
dc.subject | invariant measure | - |
dc.subject | Dobrushin’s ergodicity coefficient | - |
dc.subject | contraction ratio | - |
dc.subject | consensus | - |
dc.subject | quantum channel | - |
dc.title | Dobrushin’s Ergodicity Coefficient for Markov Operators on Cones | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s00020-014-2193-2 | - |
dc.identifier.scopus | eid_2-s2.0-84922106140 | - |
dc.identifier.volume | 81 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 127 | - |
dc.identifier.epage | 150 | - |
dc.identifier.isi | WOS:000347161500006 | - |
dc.identifier.issnl | 0378-620X | - |