Aging in two-dimensional Bouchaud's model

Let E-x be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on Z(2) is a Markov chain X(t) whose transition rates are given by w(xy) = nu exp (-beta E-x) if x, y are neighbours in Z(2). We study the behaviour of two correlation functions: P[X(t(w)+t) = X(t(w))] and P[X(t') = X(t(w)) for all t'is an element of [t(w), t(w) + t]]. We prove the (sub)aging behaviour of these functions when beta > 1.