Directed random walks in random environments

Asymptotics for directed random walks in random environments

“…We note that (3.42) was also proven by Buffet and Hannigan [4] under much stronger moment condition than Ewo 2 < ~c.…”

“…Buffet and Hannigan [4] points out that directed random walks in random environments are mainly used as "models for the motion of electrons in crystals with impurities. Buffet and Hannigan [4] points out that directed random walks in random environments are mainly used as "models for the motion of electrons in crystals with impurities.…”

“…Buffet and Hannigan [4] points out that directed random walks in random environments are mainly used as "models for the motion of electrons in crystals with impurities. Using holding times, Buffet and Hannigan [4] gave a simple representation for X(t). Because the nature and location of the defects can only be controlled in a statistical sense, their effect is best taken into account by treating the transition rates of the walk as random variables."…”

A local limit theorem for a transient chaotic walk in a frozen environment

“…Solomon [35]; Kesten, Kozlov, and Spitzer [25]), whereas the literature on quenched central limit theorems is more recent. Buffet and Hannigan [8] proved a quenched central limit theorem for a pure birth process in an independently scattered random environment under moment conditions later relaxed by Horváth and Shao [21,22]; this model is a direct continuous-time analogue of the random walk studied here. Quenched central limit theorems for more general one-dimensional transient random walks were proved only very recently, independently by Goldsheid [17] and Peterson [30] (see also Alili [1] for a result concerning a special quasiperiodic environment).…”