Variational functionals appear in several discrete and continuous random models. One of particular interest is the action functional S(x,y,t,ω) = inf ∫t0 L(ξ',ξ,ω) ds, where the infimum is taken over all smooth curves ξ satisfying ξ(0) = y and ξ(t) = x. In dimension 1, the results of Rezakhanlou imply that S(0,nq,nt,ω) satisfies the...