On the asymptotical normality of statistical solutions for harmonic crystals in half-space
Tatiana Vladimirovna Dudnikova · Russian Journal of Mathematical Physics · 2008
We consider the dynamics of a harmonic crystal in the half-space with zero boundary condition. It is assumed that the initial date is a random function with zero-mean, finite-mean energy density which also satisfies a mixing condition of Rosenblatt or Ibragimov type. We study the distribution µ t of the solution at time t ∈ ℝ. The main result is the convergence of µ t as t → ∞ to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian in general).