  We consider a population of $N$ labeled random walkers moving on a substrate,
and an excitation jumping among the walkers upon contact. The label
$\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be
viewed as a stochastic process, where the transition probabilities are a
stochastic process themselves. Upon mapping onto two simpler processes, the
quantities characterizing $\mathcal{X}(t)$ can be calculated in the limit of
long times and low walkers density. The results are compared with numerical
simulations. Several different topologies for the substrate underlying
diffusion are considered.
