  Consider orthogonal planes in the 3-D space representing floors and walls in
a large building. These planes divide the space into rooms where a wireless
infrastructure is deployed. This paper is focused on the analysis of the
correlated shadowing field created by this wireless infrastructure through the
set of walls and floors. When the locations of the planes and of the wireless
nodes are governed by Poisson processes, we obtain a simple stochastic model
which captures the non-uniform nature of node deployment and room sizes. This
model, which we propose to call the Poisson building, captures the complex
in-building shadowing correlations, is scalable in the number of dimensions and
is tractable for network performance analysis. It allows an exact mathematical
characterization of the interference distribution in both infinite and finite
buildings, which further leads to closed-form expressions for the coverage
probabilities in in-building cellular networks and the success probability of
in-building underlay D2D transmissions.
