Inhomogeneous ensembles of correlated random walkers

x j for each member j of the ensemble. We show that two ensembles [t; f(qj;x j)g] and t 0 ; (q 0;x 0) dened at dierent time intervals t 6 t 0 can have the same statistical properties at long lagtimes t, if their parameters are related by a certain scaling transformation. Finally, we argue that similar statistical properties are expected for homogeneous ensembles, in which the parameters (qj(t);x j(t)) of each individual walker uctuate temporarily, provided the parameters can be considered constant for time periods T t longer than the considered lagtime t. Similar models are applicable to many complex systems in which the individual agents undergo distinct - yet aysnchronous - behavioural phases, so that the statistics of the ensemble as a whole can still be considered as stationary.