Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155789 | Stochastic Processes and their Applications | 2011 | 21 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Lasse Leskelä, Mikko Stenlund,