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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.

MSC:
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
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