  We study map lattices coupled by collision and show how perturbations of
transfer operators associated with the spatially periodic approximation of the
model can be used to extract information about the complete system. More
precisely, we first study a map on a finite box of $L$ sites with periodic
boundary conditions, coupled by collision. We derive, via a non-trivial first
order approximation for the leading eigenvalue of the rare event transfer
operator, a formula for the first collision rate and a corresponding first
hitting time law. For the former we show that the formula scales at the order
of $L\cdot\varepsilon^2$, where $\varepsilon$ is the coupling strength, and for
the latter we show that the error in the law is of order
$O\left(L\varepsilon^2\cdot|\ln L\varepsilon^2|\right)$. Using this
information, we then derive an explicit formula for the first collision rate
per lattice unit in the infinite dimensional system
