As a microscopic model we consider a system of interacting continuum like spin field over Rd. Its evolution law is determined by the Ginzburg-Landau type random Hamiltonian and the total spin of the system is preserved by this evolution. We show that the spin field converges, under the hydrodynamic space-time scalling, to a deterministic limit which is a solution of a certain nonlinear diffusion equation. This equation describes the time evolution of the macroscopic field. The hydrodynamic scaling has an effect of the homogenization on the system at the same time.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty