above describes the behavior of random walkers who, while exploring the lattice, get trapped in the potential wells. Once trapped at site $k$, they have to wait for a time $\tau$ (actual waiting time) with pdf $$\begin{aligned}
   \psi_k (\tau) &= \frac{1}{\tau_k} \exp\left(-\frac{\tau}{\tau_k}\right),
   \label{equ:exponentialpdf}
  \end{aligned}$$ containing the mean waiting time $\tau_k$ at a site $k$ as parameter. Note that these local means $\tau_k$ are distributed according to Eq. (\[equ:rhotau\]) and the exponential waiting time density of Eq. (\[equ:exponentialpdf\]) is already conditioned on the fact that a random walker resides on a site with mean waiting time $\tau_k$. After the random walkers have waited long enough, they jump with equal probability to any of the recent site’s neighbors. Thus, the spatial properties of each single random walker’s trajectory are the same as in a simple random walk on the lattice. What is interesting, is the temporal evolution. The single-particle (one-time) quantities such as the mean squared displacement are well-understood, and can in high dimensions be described by the continuous-time random walk scheme; the behavior in 1D, which shares many properties with the CTRW behavior, is also well-investigated [@Bouchaud1990]. The properties of the motion of two or more random walkers exploring the same 