On the Zero-Type property and mixing of Bernoulli shifts

2010/01/24 by Zemer Kosloff, Kosloff, Zemer
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.1001.4261

10 pages, An example of a power weakly mixing Bernoulli shift added. A reference to other examples of zero type and type III transformations was added. An example of a power weakly mixing flow is added

openalex publication_date 2010/01/24 · arxiv created 2011/03/06 · arxiv updated 2011/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every non-singular Bernoulli shift is either zero-type or there is an equivalent invariant stationary product probability. We also give examples of a type Bernoulli shift and a Markovian flow which are power weakly mixing and zero type.

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