energy landscape are much less understood.

In what follows we concentrate on some of these multiparticle quantities, from which the (inverse) participation ratio $Y_2(t)$, which represents the probability that two random walkers who started at $t_0 = 0$ at the same site $k_0$ meet again at time $t$, was considered the most interesting. If the lattice is finite, the disorder-averaged long-time limit $\lim_{t \rightarrow \infty} \langle Y_2 (t)\rangle_\tau$ converges to an equilibrium value $\langle Y_2 \rangle_\tau^{(eq)} = 1-\alpha$ [@Bertin2002; @Derrida1997], independent of the lattice’s dimension $D$. The question about the non-equilibrium behavior of $\langle Y_2 \rangle_\tau$, however, is much more involved. It seems especially fascinating that in dimension one even for infinitely large lattices there exist a finite disorder-averaged long-time limit $\langle Y_2 \rangle_\tau^{(dyn)} >0$ with $\langle Y_2 \rangle_\tau^{(dyn)} \neq \langle Y_2 \rangle_\tau^{(eq)}$, the phenomenon called *dynamical localization*. This manifests itself also in finite but large one-dimensional lattices as a pronounced plateau in the temporal evolution of $\langle Y_2\rangle_\tau$ (see Fig. \[fig:Y2p0av\]). The existence of this regime has been mathematically proven by Fontes *et al.* [@Fontes2002] and was further investigated by Bertin and Bouchaud [@Bertin2002]. For lattices with dimension $D \geq 3$, Fontes *et al.* [@Fontes1999] proved that the dynamical 