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Central limit theorem and cohomological equation on homogeneous spaces

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Abstract

The dynamics of one-parameter diagonal group actions on finite volume homogeneous spaces has a partially hyperbolic feature. In this paper we extend the Livšic-type result to these possibly noncompact and nonaccessible systems. We also prove a central limit theorem for the Birkhoff averages of points on a horospherical orbit. The Livšic-type result allows us to show that the variance of the central limit theorem is nonzero provided that the test function has nonzero mean with respect to an invariant probability measure.

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Acknowledgements

I would like to thank Seonhee Lim, Weixiao Shen and Jiagang Yang for discussions related to this work.

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Authors and Affiliations

  1. Shanghai Center for Mathematical Sciences, Jiangwan Campus, Fudan University, No. 2005 Songhu Road, Shanghai, 200433, China

    Ronggang Shi

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  1. Ronggang Shi
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Correspondence to Ronggang Shi.

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The author is supported by NSFC 11871158.

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Shi, R. Central limit theorem and cohomological equation on homogeneous spaces. Isr. J. Math. 242, 891–931 (2021). https://doi.org/10.1007/s11856-021-2152-y

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  • DOI: https://doi.org/10.1007/s11856-021-2152-y

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