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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	165
Journal	Communications in Mathematical Physics
Volume	407
Issue number	8
DOIs	https://doi.org/10.1007/s00220-026-05667-5
Publication status	Published - 2026 Aug

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-026-05667-5

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title = "Annealed and Quenched Representations of the Gauss{\textendash}R{\'e}nyi Measure by {\textquotedblleft}Periodic Points{\textquotedblright}",

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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Y1 - 2026/8

N2 - 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.

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”

Abstract

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