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An effective criterion and a new example for ballistic diffusions in random environment. (English) Zbl 1149.60068
Random walks in a random environment are studied in multidimensional setting with the purpose of establishing local characterizations for an emergence of ballistic diffusions. A complete characterization of a ballistic behavior in the one-dimesional case is available due to F. Solomon [Ann. Probab. 3, 1–31, (1975; Zbl 0305.60029)]. In higher dimensions such a characterization is as yet incomplete and, for transient random walks in a random environment, an effective criterion (in fact two of them) for an asymptotically ballistic behavior was formulated by A.-S. Sznitman (2003), implying a ballistic law of large numbers and a central limit theorem. In the present paper an effective local criterion is proposed and suitable perturbed Brownian motions are introduced to provide new examples of diffusions with a ballistic behavior, beyond prior knowledge.

MSC:
60K37 Processes in random environments
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
60J60 Diffusion processes
60G60 Random fields
60F05 Central limit and other weak theorems
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