  It is well known that random walks in one dimensional random environment can
exhibit subdiffusive behavior due to presence of traps. In this paper we show
that the passage times of different traps are asymptotically independent
exponential random variables with parameters forming, asymptotically, a Poisson
process. This allows us to prove weak quenched limit theorems in the
subdiffusive regime where the contribution of traps plays the dominating role.
