Assume you have a Poisson point process of constant intensity $\lambda$ in the Euclidean plane. From this point process we construct the Delaunay triangulation (or the Voronoi tessellation for that matter).
It is known [Stoyan et all] that the expected degree of a typical vertex has degree 6. Moreover, there are several results for the average area of a typical triangle, edge lengths and so on. However, all the results seem to be for constant intensity. My question is: Is it known how the expected degree changes as we change the intensity?
More specifically, assume we have a rotationally invariant intensity $\rho(r)$ where $r$ is the distance to the origin and assume that $\rho(r)\to\infty$ as $r$ increases. How, does the expected degree of a node depends on its distance to the origin. The intuition is that the degree is going to increase as $r$ increases but is there any known result or reference in this direction? This is not my research area so I will appreciate any help or comment!