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

Macroscopic Wave Propagation for 2D Lattice with Random Masses