A note on the ballistic limit of random motion in a random potential

Markus Flury (University of Tuebingen)

Abstract


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.

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Pages: 393-400

Publication Date: June 27, 2008

DOI: 10.1214/ECP.v13-1394

References

  1. M. Flury. Large deviations and phase transition for random walks in random nonnegative potentials. Stochastic Process. Appl. 117 (2007), no. 5, 596--612. MR2320951
  2. A.S. Sznitman. Brownian motion, obstacles, and random media. Springer Mongraphs in Mathematics. Springer-Verlag, Berlin, 1998. xvi+353 pp. ISBN: 3-540-64554-3 MR1717054 (2001h:60147)
  3. M.P.W. Zerner. Directional decay of the Green's function for a random nonnegative potential on $Z^d$. Ann. Appl. Probab. 8 (1998), no. 1, 246--280. MR1620370 (99f:60172)
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