Limit distributions of the states and homogenization in random media (Q1179864)

The author deals with some homogenization problems in random media. An asymptotic definition of a statistically homogeneous medium is obtained by comparing the probability measures of the local ``states'' in different samples: a definition of ``representative'' samples is given. The proposed approach consists in a transport of the homogenization problem from the physical space to the space of states. A variational model is proposed for statistically homogeneous media with potential local response, generalizing a model for plastically deformed polycrystals. In this case a single parameter of the average local inhomogeneity is sufficient to set an exact statistical solution between the two extreme bounds of the average potential.