2013/11/30 by Anthony Quas, Terry Soo
Computer Science · Mathematics · #Bernoulli scheme #Bernoulli's principle #Cellular Automata and Applications #Entropy (arrow of time) #Ergodic theory #Mathematical Dynamics and Fractals #Measure (data warehouse) #Monotone polygon #Stochastic processes and statistical mechanics #math.DS #math.PR
paper · pdf · doi:10.1214/14-aop968
published as Annals of Probability 2016, Vol. 44, No. 1, 107-130 · Published at http://dx.doi.org/10.1214/14-AOP968 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2016/01/01 · arxiv created 2016/02/15 · arxiv updated 2016/02/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.