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<p>We study independently identically distributed random compositions of the Gauss and Rényi maps that are related to Diophantine approximation. Elaborating on methods in ergodic theory, thermodynamic formalism and large deviations, we prove that weighted cycles of this random dynamical system equidistribute with respect to the Gauss–Rényi measure. We obtain both annealed (sample-averaged) and quenched (samplewise) results.</p>

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Annealed and Quenched Representations of the Gauss–Rényi Measure by “Periodic Points”

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Shintaro Suzuki,
  • Hiroki Takahasi

摘要

We study independently identically distributed random compositions of the Gauss and Rényi maps that are related to Diophantine approximation. Elaborating on methods in ergodic theory, thermodynamic formalism and large deviations, we prove that weighted cycles of this random dynamical system equidistribute with respect to the Gauss–Rényi measure. We obtain both annealed (sample-averaged) and quenched (samplewise) results.