Given a locally finite set of points $\{x_1,x_2,\dots\}\subset\mathbb{R}^d$, the Voronoi cell of a point $x_{i}$, denoted by $C(x_{i})$, consists of all the points in $\mathbb{R}^d$ that are closer to $x_i$ than to any other point $x_j$. The partition of the whole space $\mathbb{R}^d$ by the Voronoi cells $C(x_i)$ is referred to as a Voronoi tessellation.
A natural extension of this construction involves replacing the points $x_{1},x_{2},\dots$ by mutually disjoint, bounded, convex sets $K_{1},K_{2},\dots\subset\mathbb{R}^{d}$ so that the (generalized) Voronoi cell of the set $K_{i}$, denoted by $C(K_{i})$, consists of all the points in $\mathbb{R}^{d}$ that are closer to $K_{i}$ than to any other set $K_{j}$. In the reference book Stochastic Geometry and its Applications, the partition of $\mathbb{R}^{d}$ by the cells $C(K_{i})$ is referred to as a Voronoi S-tessellation.
A lot is known about the statistics of random Voronoi tessellations when the underlying points $x_{i}$ are sampled from a Poisson point process. Statistical quantities such as the mean volume of a typical Voronoi cell have been explicitly computed as functions of the intensity $\lambda$ of the Poisson point process (see Chapter 9 of Stochastic Geometry and its Applications). In contrast, much less seems to be known about random Voronoi S-tessellations, in particular, when the sets $K_{i}$ are taken to be identical disks ($d=2$) or balls ($d=3$), as one would get by sampling from a Gibbs point process with hard-sphere interactions (again at some intensity $\lambda$). Indeed, in this case, online searches yield mostly simulation results and non-rigorous, heuristic arguments.
I am wondering if there is any known rigorous result on the statistics of such random Voronoi S-tessellations (e.g., the mean volume of a typical Voronoi cell) or any rigorous method that may be relevant, especially those applicable to large $\lambda\gg1$.