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

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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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 (2009). https://doi.org/10.1007/s12044-009-0052-x

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Keywords

  • Packing dimension
  • stochastic matrices
  • Erdös sum
  • products of random matrices
  • continuous singularity of the limit distribution