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A note on the ballistic limit of random motion in a random potential. (English) Zbl 1187.60091
Summary: It has been shown that certain types of random walks in random potentials and Brownian motion in Poissonian potentials undergo a phase transition from sub-ballistic to ballistic behavior when the strength of the underlying drift is increased. The ballistic behavior has been manifested by indicating a limiting area for the normalized motion. In the present article, we provide a refined description of this limiting area with a further development for the case of rotation invariant Poissonian potentials.

MSC:
60K37 Processes in random environments
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