Transfer Operators and Limit Laws for Typical Cocycles

Kiho Park; Mark Piraino

doi:10.1007/s00220-021-04300-x

Transfer Operators and Limit Laws for Typical Cocycles

Kiho Park^*, Mark Piraino

^*Corresponding author for this work

Mathematics

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

5 Scopus citations

Abstract

We show that typical cocycles (in the sense of Bonatti and Viana) over irreducible subshifts of finite type obey several limit laws with respect to the unique equilibrium states for Hölder potentials. These include the central limit theorem and the large deviation principle. We also establish the analytic dependence of the top Lyapunov exponent on the underlying equilibrium state. The transfer operator and its spectral properties play key roles in establishing these limit laws.

Original language	English (US)
Pages (from-to)	1475-1523
Number of pages	49
Journal	Communications in Mathematical Physics
Volume	389
Issue number	3
DOIs	https://doi.org/10.1007/s00220-021-04300-x
State	Published - Feb 2022

Funding

M.P. was supported in part by the National Science Foundation Grant “RTG: Analysis on manifolds” at Northwestern University.

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-021-04300-x

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N2 - We show that typical cocycles (in the sense of Bonatti and Viana) over irreducible subshifts of finite type obey several limit laws with respect to the unique equilibrium states for Hölder potentials. These include the central limit theorem and the large deviation principle. We also establish the analytic dependence of the top Lyapunov exponent on the underlying equilibrium state. The transfer operator and its spectral properties play key roles in establishing these limit laws.

AB - We show that typical cocycles (in the sense of Bonatti and Viana) over irreducible subshifts of finite type obey several limit laws with respect to the unique equilibrium states for Hölder potentials. These include the central limit theorem and the large deviation principle. We also establish the analytic dependence of the top Lyapunov exponent on the underlying equilibrium state. The transfer operator and its spectral properties play key roles in establishing these limit laws.

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Transfer Operators and Limit Laws for Typical Cocycles

Abstract

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