Random walks in a random environment. (English) Zbl 1077.60078

This is a short survey on well-known results on random walks in a random environment, and it announces and concisely explains new results on large-deviation estimates, which will appear in a separate paper (joint work with Kosygina and Rezakhnalou). The paper recalls basic facts and results on usual random walks, introduces the concept of random walks in random environments and recalls by now well-known results on that subject (laws of large numbers, central limit theorems, large deviations, both quenched and annealed). An annealed large-deviation principle (derived recently by the author using an innovative method) is outlined. Finally, and this is the new part of the paper, the proof of a quenched large-deviation principle is outlined in the framework of Brownian motion with a random drift. The precise assumptions and the details of the proof will appear elsewhere.


60K37 Processes in random environments
60G50 Sums of independent random variables; random walks
60F10 Large deviations
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