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 ${\varphi }_{\mathrm{a}\mathrm{v}\mathrm{g}}$ ranges from 0.8175 to 0.8380. We observe short-ranged correlations over the whole range of $\phi_{\rm avg}$andanti-correlationsfor$\phi_{\rm avg}>0.8277$. The spatial extent of the anti-correlation increases with ${\varphi }_{\mathrm{a}\mathrm{v}\mathrm{g}}$ while the position of the maximum of the anti-correlation and the extent of the positive correlation shrink with ${\varphi }_{\mathrm{a}\mathrm{v}\mathrm{g}}$. We conjecture that the onset of anti-correlation corresponds to dilatancy onset in this system.