Ergodic Properties of the Random Walk Adic Transformation over the Beta Transformation

2015/11/08 by Michael Bromberg, Bromberg, Michael
Computer Science · Mathematics · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories #math.DS

paper · pdf · doi:10.48550/arxiv.1511.02482

openalex publication_date 2015/11/08 · arxiv created 2015/11/22 · arxiv updated 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a random walk adic transformation associated to an aperiodic random walk on G=ℤ^k×ℝ^D-k driven by a β-transformation and study its ergodic properties. In particular, this transformation is conservative, ergodic, infinite measure preserving and we prove that it is asymptotically distributionally stable and bounded rationally ergodic. Related earlier work appears in [AS] and [ANSS] for random walk adic transformations associated to an aperiodic random walk driven by a subshift of finite type.

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