Polynomial rate of mixing for the heterochaos baker maps with mostly neutral center

2024/08/29 by Hiroki Takahasi, Takahasi, Hiroki, Masato Tsujii +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2408.16618

openalex publication_date 2024/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the heterochaos baker maps whose central direction is mostly neutral, we prove that correlations for Hölder continuous functions decay at an optimal polynomial rate of order n^-3/2. Our method of proof relies on a description of the action of a reduced Perron-Frobenius operator by means of a comparison to the symmetric simple random walk with an absorbing wall, aka `gambler's ruin problem'.

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