  In this paper, we consider a class of two-particle tight-binding
Hamiltonians, describing pairs of interacting quantum particles on the lattice
$\Z^d$, $d\ge 1$ subject to a common external potential $V(x)$ which we assume
quasi-periodic and depending on an auxiliary parameter. Such parametric
families of ergodic deterministic potentials ("grand ensembles") have been
introduced earlier in \cite{C07}, in the framework of single-particle lattice
systems, where it was proved that a non-uniform analog of the Wegner bound
holds true for a class of quasi-periodic grand ensembles. Using the approach
proposed in \cite{CS08}, we establish volume-dependent Wegner-type bounds for a
class of quasi-periodic two-particle lattice systems with a non-random
short-range interaction.
