Deterministic walks in random environments

• Published in: Physica. D Vol. 187; no. 1; pp. 20 - 29
• Main Author: Bunimovich, Leonid A
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 2004; Elsevier
• Subjects: Cellular automata; Classical chaos; Classical transport; Deterministic walks; Exact sciences and technology; Lorentz lattice gases; Nonlinear dynamics and nonlinear dynamical systems; Physics; Random environments; Random walks; Statistical physics, thermodynamics, and nonlinear dynamical systems; Transport processes; 05.40.Fb; Random environments; Random walks; 05.45.Tp; Cellular automata; Lorentz lattice gases; 05.60.Cd; Deterministic walks; Random walk; Diffusion process; Deterministic system; Orbits; Transport processes; Random media; Dynamical systems
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2003.09.028

Deterministic walks in random environments (DWRE) occupy an intermediate position between purely random (generated by random trials) and purely deterministic (generated by deterministic dynamical systems, e.g., by maps) models of diffusion. These models combine deterministic and probabilistic features. We review general properties of DWRE and demonstrate that, to a large extent, their dynamics and their statistics can be analyzed consecutively and separately. We also show that orbits of one-dimensional walks in rigid environments with non-constant rigidity almost surely visit each site infinitely many times.