Small-world behaviour in a system of mobile elements

We analyze the propagation of activity in a system of mobile automata. A nu mber rhoL(d) of elements move as random walkers on a lattice of dimension d , while with a small probability p they can jump to any empty site in the s ystem. We show that this system behaves as a Dynamic Small World (DSW) and present analytic and numerical results for several quantities. Our analysis shows that the persistence time T* (equivalent to the persistence size L* of small-world networks) scales as T* similar to (rhop)(-tau), with tau = 1 /(d + 1).