  First passage time statistics in disordered systems exhibiting scale
invariance are studied widely. In particular, long trapping times in energy or
entropic traps are fat-tailed distributed, which slow the overall transport
process. We study the statistical properties of the first passage time of
biased processes in different models, and employ the big jump principle that
shows the dominance of the maximum trapping time on the first passage time.
Inspired by the restart paradigm, we demonstrate that the removal of this
maximum significantly expedites transport. As the disorder increases, the
system enters a phase where the removal shows a dramatic effect. Our results
show how we may speed up transport in strongly disordered systems exploiting
scale invariance. In contrast to the disordered systems studied here, the
removal principle has essentially no effect in homogeneous systems; this
indicates that improving the conductance of a poorly conducting system is,
theoretically, relatively easy as compared to a homogeneous system.
