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We analyze the propagation of activity in a system of mobile automata. Anumber r L^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 system.We show that this system behaves as a Dynamic Small-World (DSW) and presentanalytic and numerical results for several quantities. Our analysis shows thatthe persistence time T* (equivalent to the persistence size L* of small-worldnetworks) scales as T* ~ (r p)^(-t), with t = 1/(d+1).Comment: To appear in Europhysics Letter

Small-world behaviour in a system of mobile elements