Correlation between Voronoi volumes in disc packings

We measure the two-point correlation of free Voronoi volumes in binary disc packings, where the packing fraction $\phi_{\rm avg}$ ranges from 0.8175 to 0.8380. We observe short-ranged correlations over the whole range of $\phi_{\rm avg}$ and anti-correlations for $\phi_{\rm avg}>0.8277$. The spatial extent of the anti-correlation increases with $\phi_{\rm avg}$ while the position of the maximum of the anti-correlation and the extent of the positive correlation shrink with $\phi_{\rm avg}$. We conjecture that the onset of anti-correlation corresponds to dilatancy onset in this system.