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A monotone Sinai theorem

Quas, A; Soo, T; (2016) A monotone Sinai theorem. The Annals of Probability , 44 (1) pp. 107-130. 10.1214/14-aop968. Green open access

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Abstract

Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy and is stochastically dominated by the original measure can be obtained as a monotone factor; that is, the factor map has the property that for each point in the domain, its image under the factor map is coordinatewise smaller than or equal to the original point.

Type: Article
Title: A monotone Sinai theorem
Open access status: An open access version is available from UCL Discovery
DOI: 10.1214/14-aop968
Publisher version: https://doi.org/10.1214/14-aop968
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Sinai factor theorem, stochastic domination, monotone coupling, Burton–Rothstein.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10089082
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