A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment

Martin P. W. Zerner (Stanford University)

Abstract


We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general law of large numbers under the only assumption of a certain zero-one law, which is known to hold if the dimension is two.

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Pages: 191-197

Publication Date: September 30, 2002

DOI: 10.1214/ECP.v7-1060

References

  1. Sznitman, A.-S. (2002), Topics in Random Walks in Random Environments. http://www.math.ethz.ch/~sznitman/topics-paper.pdf (preprint) Math. Review number not available.
  2. Sznitman, A.-S. and Zerner, M.P.W. (1999), A law of large numbers for random walks in random environment. Ann. Probab. 27, no. 4, 1851-1869 Math. Review 2001f:60116
  3. Zeitouni, O. (2001), Notes on Saint Flour Lectures 2001. http://www.ee.technion.ac.il/~zeitouni/ps/notes1.ps (preprint) Math. Review number not available.
  4. Zerner, M.P.W. and Merkl, F. (2001), A zero-one law for planar random walks in random environment. Ann. Probab. 29, No. 4, 1716-1732 Math. Review number not available.
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