  We consider a random walk among a Poisson cloud of moving traps on ${\mathbb
Z}^d$, where the walk is killed at a rate proportional to the number of traps
occupying the same position. In dimension $d=1$, we have previously shown that
under the annealed law of the random walk conditioned on survival up to time
$t$, the walk is sub-diffusive. Here we show that in $d\geq 6$ and under
diffusive scaling, this annealed law satisfies an invariance principle with a
positive diffusion constant if the killing rate is small. Our proof is based on
the theory of thermodynamic formalism, where we extend some classic results for
Markov shifts with a finite alphabet and a potential of summable variation to
the case of an uncountable non-compact alphabet.
