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A local limit theorem for a transient chaotic walk in a frozen environment

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  • Leskelä, Lasse
  • Stenlund, Mikko

Abstract

This paper studies particle propagation in a one-dimensional inhomogeneous medium where the laws of motion are generated by chaotic and deterministic local maps. Assuming that the particle’s initial location is random and uniformly distributed, this dynamical system can be reduced to a random walk in a one-dimensional inhomogeneous environment with a forbidden direction. Our main result is a local limit theorem which explains in detail why, in the long run, the random walk’s probability mass function does not converge to a Gaussian density, although the corresponding limiting distribution over a coarser diffusive space scale is Gaussian.

Suggested Citation

  • Leskelä, Lasse & Stenlund, Mikko, 2011. "A local limit theorem for a transient chaotic walk in a frozen environment," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2818-2838.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:12:p:2818-2838
    DOI: 10.1016/j.spa.2011.07.010
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    References listed on IDEAS

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    1. Jorváth, Lajos & Shao, Qi-Man, 1994. "A note on the law of large numbers for directed random walks in random environments," Stochastic Processes and their Applications, Elsevier, vol. 54(2), pages 275-279, December.
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