Stability problems in multi-component random systems

The main topic of our talk is the stability of multi-component random systems with respect to 1) random external influence or 2) random perturbation of the initial data. Hamiltonian systems of point particles with special interaction potential will be used as an essential model of multi-component random systems. At first, we will discuss a stability problem with respect to random external noises: formulate several results about convergence to equilibrium, describe resonances (transience) and conditions for them. Convergence to equilibrium we associate with stability (however, in some sense it quite unjustified). A couple of groups of external noises will be considered: white noise, Gaussian processes, flips, elastic collisions. In the second part of our talk, we will consider a regularity property (non-intersection of trajectories) for multi-component random systems. We will discuss how perturbations (random and deterministic) of the initial data affect this property. We will show some applications of the regularity property to the problem of the derivation of hydrodynamic equations and traffic flow problems.