We investigate the ergodic properties of Hamiltonian systems subjected to local random, energy conserving perturbations. We prove for some cases, e.g. anharmonic crystals with random nearest neighbor exchanges (or independent random reflections) of velocities, that all translation invariant stationary states with finite entropy per unit volume are microcanonical Gibbs states. The results can be utilized in proving hydrodynamic behavior of such systems.
- Mathematics Subject Classification (1991): 60K35, 82A05
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty