A sluggish random walk with subdiffusive spread

We study a one-dimensional sluggish random walk with space-dependent transition probabilities between nearest-neighbour lattice sites. Motivated by trap models of slow dynamics, we consider model in which the depth increases logarithmically distance from origin. This leads to has symmetric that decrease $|k|$ origin as $1/|k|$ for large $|k|$. show typical position after time $t$ scales $t^{1/3}$ nontrivial scaling function distribution trough (a cusp singularity) at Therefore an effective central bias away emerges even though are symmetric. also compute survival probability walker presence sink and it decays $t^{-1/3}$ late times. Furthermore maximum position, $M(t)$, right up $t$, function. Finally provide generalisation this where decay $1/|k|^\alpha$ $\alpha >0$.