Excitations Transfer and Random Walks on Dynamic Contacts Networks

Diffusion and spreading processes are strongly influenced by the topology of the substrate. An interesting example is provided by exchange reactions in the diffusion-limited regime, that model the spreading of an excitation among a population of randomly moving agents. In this case, the excitation is diffusing on an evolving dynamical graph, created by the istantaneous contacts of the moving agents. In recent works, the excitation random walk on the contacts graph generated by a set of random walkers moving on restricted geometries has been considered. We review here the properties of the process and we extend our results to the case of multiple excitations transfer with fermionic and bosonic statistics.