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

Shintaro Suzuki; Hiroki Takahasi

doi:10.1007/s00220-026-05667-5

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

Shintaro Suzuki
, Hiroki Takahasi

数理科学科

研究成果: Article › 査読

抄録

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.

本文言語	English
論文番号	165
ジャーナル	Communications in Mathematical Physics
巻	407
号	8
DOI	https://doi.org/10.1007/s00220-026-05667-5
出版ステータス	Published - 2026 8月

ASJC Scopus subject areas

統計物理学および非線形物理学
数理物理学

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10.1007/s00220-026-05667-5

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abstract = "We study independently identically distributed random compositions of the Gauss and R{\'e}nyi 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{\textendash}R{\'e}nyi measure. We obtain both annealed (sample-averaged) and quenched (samplewise) results.",

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AB - 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.

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

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