  We consider a simple two-dimemsional harmonic lattice with random,
independent and identically distributed masses. Using the methods of stochastic
homogenization, we show that solutions with long wave initial data converge in
an appropriate sense to solutions of an effective wave equation. The
convergence is strong and almost sure. In addition, the role of the lattice's
dimension in the rate of convergence is discussed. The technique combines
energy estimates with powerful classical results about sub-Gaussian random
variables.
