Large deviations for one-dimensional random walk in a random environment - a survey
نویسنده
چکیده
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment deenes a random walk fX n g (called a RWRE) which, when at x, moves one step to the right with probability ! x , and one step to the left with probability 1 ? ! x. Solomon (1975) determined the almost-sure asymptotic speed v (=rate of escape) of a RWRE. Subsequent work provided limit theorems for the RWRE fX n g. We review in this article recent results on the asymptotics of the probability of rare events of the form P(X n =n 2 A) or P ! (X n =n 2 A), in the situation where P(X n =n 2 A) ?! n!1 0. It turns out that the RWRE exhibits a wide range of non-trivial behavior, and diierent regimes are possible.
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