We investigate sub-diffusion in the quenched trap model by an interesting  time transformation. We map the random walk in the disordered environment  onto a new stochastic process:  Brownian motion stopped at the operational time ${\cal S}_\alpha = \sum_{x=-\infty} ^\infty (n_x)^\alpha$ where $n_x$ is the visitation number at site $x$ and $\alpha=T/T_g <1$ is a measure of the disorder. In the limit of zero temperature we recover the renormalization group (RG) solution found by Monthus. Our approach is an alternative to RG capable of dealing with any disorder strength.

Burov, Barkai PRL 106 140602 (2011).