Velocity and Lyapunov exponents of some random walks in random environment (Q1594508)

The author links two different concepts concerning the asymptotic behavior of multidimensional random walks in random environment satisfying Kalikow's condition. First, an expression for the asymptotic velocity of the random walk can be derived using some renewal times, law of large numbers and central limit theorem for the walk [see \textit{A.-S. Sznitman} and the author, Ann. Probab. 27, No. 4, 1851-1869 (1999; Zbl 0965.60100)]. Second, certain Lyapunov exponents are used to obtain the rate function for some large deviation principle for the walk [see the author, ibid. 26, No. 4, 1446-1476 (1998; Zbl 0937.60095)]. An alternative expression for the asymptotic velocity of the walk is given in terms of the Lyapunov exponents.