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

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

2011-08-19

arxiv.org/abs/1108.3925v1

Stochastic Processes and their Applications 121 (2011) 2818-2838

Mathematics

Probability

26 pages, 2 figures. To appear in Stochastic Processes and their Applications

Scientific paper

10.1016/j.spa.2011.07.010

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.

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