Random walks in media with constrained disorder

The authors have considered in the framework of the field-theoretical approach the asymptotics of random walks in media with quenched disorder which is described by drift velocity field V(x) subjected to various constraints. The disorder has proved to be relevant in d<or=2 dimensions leading (at d=2) to superdiffusion behaviour for the solenoidal random drift ( delta Vi/ delta xi=0) and to subdiffusion behaviour for the potential random drifts ( delta Vi/ delta xj- delta Vj/ delta xi=0).