On the asymptotical normality of statistical solutions for wave equations coupled to a particle

摘要

We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein-Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function which has some mixing properties. We study the distribution mu (t) of the random solution at time moments t a R. The main result is the convergence of mu (t) to a Gaussian probability measure as t -> a. The application to the case of Gibbs initial measures is given.