Deterministic walks in random environments

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 featur...

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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
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Abstract	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.
AbstractList	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.
Author	Bunimovich, Leonid A
Author_xml	– sequence: 1 givenname: Leonid A surname: Bunimovich fullname: Bunimovich, Leonid A email: bunimovh@math.gatech.edu organization: Department of Mathematics, Southeast Applied Analysis Center, Georgia Institute of Technology, Atlanta, GA 30332, USA
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Cites_doi	10.1016/0167-2789(86)90237-X 10.1007/BF02046760 10.1007/BF01049035 10.1137/1127028 10.1103/PhysRevLett.86.5417 10.1007/BF01942372 10.1023/A:1024623827182 10.1016/S0378-4371(99)00518-X 10.1007/BF02186805 10.1070/RM1991v046n04ABEH002827 10.1070/RM1990v045n03ABEH002355 10.1023/A:1004611208149 10.1007/BF01048051 10.1007/BF01008951 10.1007/BF01060071 10.1007/BF02099254 10.1023/A:1010409913034 10.1088/0305-4470/18/17/006 10.1023/A:1026581213671 10.1023/A:1019727111513
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Keywords	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
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SubjectTerms	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
Title	Deterministic walks in random environments
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