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We consider a linear Fermi-Pasta-Ulam-Tsingou lattice with random spatiallyvarying material coefficients. Using the methods of stochastic homogenizationwe show that solutions with long wave initial data converge in an appropriatesense to solutions of a wave equation. The convergence is strong and bothalmost sure and in expectation, but the rate is quite slow. The techniquecombines energy estimates with powerful classical results about random walks,specifically the law of the iterated logarithm.

Using Random Walks to Establish Wavelike Behavior in an FPUT System with Random Coefficients