  We study the statistical behavior of two out of equilibrium systems. The
first one is a quasi one-dimensional gas with two species of particles under
the action of an external field which drives each species in opposite
directions. The second one is a one-dimensional spin system with nearest
neighbor interactions also under the influence of an external driving force.
Both systems show a dynamical scaling with domain formation. The statistical
behavior of these domains is compared with models based on the coalescing
random walk and the interacting random walk. We find that the scaling domain
size distribution of the gas and the spin systems is well fitted by the Wigner
surmise, which lead us to explore a possible connection between these systems
and the circular orthogonal ensemble of random matrices. However, the study of
the correlation function of the domain edges, show that the statistical
behavior of the domains in both gas and spin systems, is not completely well
described by circular orthogonal ensemble, nor it is by other models proposed
such as the coalescing random walk and the interacting random walk.
Nevertheless, we find that a simple model of independent intervals describe
more closely the statistical behavior of the domains formed in these systems.
