Local Limit Theorems for Random Walks in a 1D Random Environment
نویسنده
چکیده
We consider random walks (RW) in a one-dimensional i.i.d. random environment with jumps to the nearest neighbours. For almost all environments, we prove a quenched Local Limit Theorem (LLT) for the position of the walk if the diffusivity condition is satisfied. As a corollary, we obtain the annealed version of the LLT and a new proof of the theorem of Lalley which states that the distribution of the environment viewed from the particle (EVFP) has a limit for a. e. environment. Mathematics Subject Classification (2010). Primary 60K37; Secondary 60F05.
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تاریخ انتشار 2013