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 Electronic Communications in Probability > Vol. 7 (2002) > Paper 19 open journal systems 


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.


Full text: PDF

Pages: 191-197

Published on: September 30, 2002
Bibliography
  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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Electronic Communications in Probability. ISSN: 1083-589X