Title: Limiting distributions for a one-dimensional random walk in a random environment.
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Abstract:
Random walks in random environments (RWRE) are a very simple model for random motion in a non-homogeneous environment. Despite the similarities between RWRE and classical random walks, RWRE can exhibit behavior that is very different from that of classical random walks. One area where this difference is apparent is in the limiting distributions of the random walks. The central limit theorem implies that the limiting distribution for classical (simple) random walks is always a Gaussian distribution. On the other hand, in my PhD thesis I showed that once a random environment is chosen, the RWRE doesn’t necessarily even have a limiting distribution. In my talk, I will discuss recent work with Gennady Samorodnitsky which helps explain why the distribution of the RWRE in a fixed environment doesn’t have a limit. Moreover, this work also shows how one can actually obtain a limiting distribution in a weaker sense.