Multiscale analysis for interacting particles: Relaxation systems and scalar conservation laws

investigate the derivation of semilinear relaxation systems and scalar cons ervation laws from a class of stochastic interacting particle systems. Thes e systems are Markov jump processes set on a lattice, they satisfy detailed mass balance (but not detailed balance of momentum), and are equipped with multiple scalings. Using a combination of correlation function methods wit h compactness and convergence properties of semidiscrete relaxation schemes we prove that, at a mesoscopic scale, the interacting particle system give s rise to a semilinear hyperbolic system of relaxation type, while at a mac roscopic scale it yields a scalar conservation law. Rates of convergence ar e obtained in both scalings.