  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 collisions per lattice unit.
More precisely, we 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, by tracking the $L$ dependency in our arguments, we show that the
error in the law is of order
$O\left(C(L)\frac{L\varepsilon^2}{\zeta(L)}\cdot\left|\ln
\frac{L\varepsilon^2}{\zeta(L)}\right|\right)$, where $\zeta(L)$ is given in
terms of the spectral gap of the rare event transfer operator, and $C(L)$ has
an explicit expression. Finally, we derive an explicit formula for the first
collision rate per lattice unit.
