We construct families of Gaussian processes xε(t,n), t ∈ [0,∞), n ∈ Z, modeling a class of infinite networks of stochastically fluctuating, interacting beads, of small mass, proportional to ε. We examine covariances E(xε(t 1 ,n 1 )xε(t 2 ,n 2 )) and draw conclusions about the subdiffusive nature of these processes, with particular attention to the behavior as ε → 0. This complements previous work of the author, which in turn was influenced by work of McKinley, Yao, and Forest.