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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n^{-3/2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>n</mi> <mrow> <mo>-</mo> <mn>3</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>. 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”.</p>

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Polynomial Rate of Mixing for the Heterochaos Baker Maps with Mostly Neutral Center

  • 期刊论文

  • 发表日期：

    2025年6月16日

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  • Hiroki Takahasi,
  • Masato Tsujii

摘要

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 \(n^{-3/2}\) 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”.