Convergence to Equilibrium Distribution. Dirac Fields Coupled to a Particle

For a system consisting of several Dirac fields and a particle, we study the Cauchy problem with random initial data. We assume that the initial measure has zero mean value, a finite mean charge density, a translation-invariant covariance and satisfies a mixing condition. The main result is the long-time convergence of distributions of the random solutions to a limit Gaussian measure.