of $\langle Y_2\rangle_{p_0, \tau}$. Fig. \[fig:RG2temporal\] depicts such a comparison with numerical averages over 100 landscape realizations.

Altogether, the phenomenon of dynamical localization is pertinent to the behavior of one, very specific localization measure. In the range of times when the dynamical localization is observed, the probability that the two independent random walkers starting at the same site appear to be at the same site at a later instant of time $t$ (as represented by $Y_2$) stagnates, but the mean squared distance between them (given by $R_G$) grows continuously. $Y_2$ is thus a measure of the concentration of the state on some small subset of sites; $R_G$, on the other hand, quantifies the size of the spatial domain in which the particles are confined. Both the dynamically localized state and the equilibrium state of the system are essentially delocalized with respect to this measure.

Localization of the eigenstates
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![The Lyapunov exponent $\gamma$ vs. inverse radius of gyration $\sqrt{\sigma^{-2}}$ (see Eq. (\[equ:sigma-2\])) on double logarithmic scales. The shaded area gives the density of single data points, whereas the dots represent averaged values. The larger circles define the ensemble for a linear fit (solid line), yielding $\log \gamma = 0.440 + 