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Upper packing dimension of a measure and the limit distribution of products of i.i.d. stochastic matrices

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Abstract

This article gives sufficient conditions for the limit distribution of products of i.i.d. 2 × 2 stochastic matrices to be continuous singular, when the support of the distribution of the individual random matrices is countably infinite. It extends a previous result for which the support of the random matrices is finite. The result is based on adapting existing proofs in the context of attractors and iterated function systems to the case of infinite iterated function systems.

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas — Pan American, 1201 West University Drive, Edinburg, TX, 78539, USA

    Arunava Mukherjea

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Ricardo Restrepo

  3. Departamento de Matemáticas, Universidad de Antioquia, Calle 67 No53-108, Medellín, Colombia, USA

    Ricardo Restrepo

Authors
  1. Arunava Mukherjea
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  2. Ricardo Restrepo
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Correspondence to Arunava Mukherjea.

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Mukherjea, A., Restrepo, R. Upper packing dimension of a measure and the limit distribution of products of i.i.d. stochastic matrices. Proc Math Sci 119, 669–677 (2009). https://doi.org/10.1007/s12044-009-0052-x

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  • DOI: https://doi.org/10.1007/s12044-009-0052-x

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