A law of large numbers for random walks in random mixing environments

By Francis Comets, Ofer Zeitouni. 2002

71 citations recorded by the source corpus.

We prove a law of large numbers for a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a weak mixing field in the sense of Dobrushin and Shlosman. Our result holds if the mixing rate balances moments of some random times depending on the path. It applies in the nonnestling case, but we also provide examples of nestling walks that satisfy our assumptions. The derivation is based on an adaptation, using coupling, of the regeneration argument of Sznitman and Zerner.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3826709c176a0d33645caf225399c7b9e21a9d7f

Citations in the corpus

• A note on multitype branching processes with immigration in a random environment (2005, unknown): “t” according to P. The claim of Theorem 1.6 is derived then from this observation. The construction used in the proof is similar to that of L-safeguards for a RWRE introduced in [17], Section 3.1 and [7]. Let ξ = (ξ n) n∈Z+ and λ = (λ (i) n,m) n∈Z+,m∈N,i=1,...,d be two collections of i.i.d. Bernoull”