  We consider a Fermi-Pasta-Ulam-Tsingou lattice with randomly varying
coefficients. We discover a relatively simple condition which when placed on
the nature of the randomness allows us to prove that small amplitude/long
wavelength solutions are almost surely rigorously approximated by solutions of
Korteweg-de Vries equations for very long times. The key ideas combine energy
estimates with homogenization theory and the technical proof requires a novel
application of autoregressive processes.

Analysis of PDEs;Dynamical Systems