Persistence in extended dynamical systems

Abstract

Persistence in spatially extended dynamical systems (like coarsening systems and other nonequilibrium systems) is reviewed. We discuss, in particular, the spatial correlations in the persistent regions and their evolution in time in these systems. We discuss the dependence of the persistence behavior on the dynamics of the system and consider the specific example of different updating rules in the temporal evolution of the system. Lastly, we discuss the universal behavior shown by persistence in various stochastic models belonging to the directed percolation universality class.