论文信息 - A NON-BALLISTIC LAW OF LARGE NUMBERS FOR RANDOM WALKS IN I.I.D. RANDOM ENVIRONMENT

A NON-BALLISTIC LAW OF LARGE NUMBERS FOR RANDOM WALKS IN I.I.D. RANDOM ENVIRONMENT

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.

M. Zerner | Martin P. W. Zerner

[1] Alain-Sol Sznitman,et al. A law of large numbers for random walks in random environment , 1999 .

[2] Franz Merkl,et al. A Zero-One Law for Planar Random walks in Random Environment , 2001 .