  Given an infinite subset $\mathcal A \subseteq\mathbb N$, let $A$ denote its
smallest $N$ elements. There is a rich and growing literature on the question
of whether for typical $\alpha\in[0,1]$, the pair correlations of the set
$\alpha A \pmod 1\subset [0,1]$ are asymptotically Poissonian as $N$ increases.
We define an inhomogeneous generalization of the concept of pair correlation,
and we consider the corresponding doubly metric question. Many of the results
from the usual setting carry over to this new setting. Moreover, the double
metricity allows us to establish some new results whose singly metric analogues
are missing from the literature.
