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Random walks in asymmetric random environments. (English) Zbl 0734.60112
Summary: We consider random walks on \({\mathbb{Z}}^ d\) with transition rates p(x,y) given by a random matrix. If p is a small random perturbation of the simple random walk, we show that the walk remains diffusive for almost all environments p if \(d>2\). The result also holds for a continuous time Markov process with a random drift. The corresponding path space measures converge weakly, in the scaling limit, to the Wiener process, for almost every p.

60K40 Other physical applications of random processes
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60G50 Sums of independent random variables; random walks
Full Text: DOI
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