  We consider a linear Fermi-Pasta-Ulam-Tsingou lattice with random spatially
varying material coefficients. Using the methods of stochastic homogenization
we show that solutions with long wave initial data converge in an appropriate
sense to solutions of a wave equation. The convergence is strong and both
almost sure and in expectation, but the rate is quite slow. The technique
combines energy estimates with powerful classical results about random walks,
specifically the law of the iterated logarithm.
