GPDs with $\zeta \neq 0$

We revisit the light-cone wave function representation for generalized parton distributions with $\zeta\neq 0$. After translating the $t$-slope into a $\Delta_\perp^2$-slope, the two-dimensional Fourier transform of GPDs is interpreted as the transition matrix element as a function of the separation between the active quark and the center of momentum of the spectators. In the limit $x\to \zeta$ it is discussed how this information can be used to learn about the dependence of the mean separation between the active quark and the spectators on the momentum fraction carried by the active quark.