STATISTICAL PROPERTIES OF SPATIOTEMPORAL DYNAMICAL-SYSTEMS

In this paper we consider spatiotemporal dynamical systems modeled by coupled, or uncoupled but noise-driven, map lattices. In particular, w e examine reports in the literature where it is found that the distrib ution of certain mean-field quantities violates the law of large numbe rs (hence nonstatistical) but not the central-limit theorem. Our resul ts show that the origin of such nonstatistical behavior is due to the statistical dependence between random variables at different lattice s ites, thus rendering nonapplicable to such situations the law of large numbers and the central-limit theorem. Additional issues explored inc lude the discussion of a special class of systems where nonstatistical behavior is not observed and the physical motivation for considering uncoupled but noise-driven map lattices.