Distribution function analysis of the structure of depleted particle configurations

We present an analysis of the $n$-particle distribution functions of a material constructed via random depletion of an arbitrary quenched state (of an equilibrium or nonequilibrium system). We show that the structure, as measured by the distribution functions $g^{\mathrm{}\left(n\right)\mathrm{}}({\mathbf{r}}_1,{\mathbf{r}}_2,\dots ,{\mathbf{r}}_n;\rho )$, is unchanged by the depletion process. Low-density configurations can thus be created with nontrivial spatial correlations inherited from a higher-density fluid. We show that this leads to an enhanced void volume and discuss implications to an irreversible adsorption process.