Abstract
We consider the combined effects of a power law Lévy step distribution characterized by the step index
f
and a power law waiting time distribution characterized by the time index
g
on the long time behavior of a random walker. The main point of our analysis is a formulation in terms of coupled Langevin equations which allows in a natural way for the inclusion of external force fields. In the anomalous case for
f<2
and
g<1
the dynamic exponent
z
locks onto the ratio
f/g
. Drawing on recent results on Lévy flights in the presence of a random force field we also find that this result is {\em independent} of the presence of weak quenched disorder. For
d
below the critical dimension
d
c
=2f−2
the disorder is {\em relevant}, corresponding to a non trivial fixed point for the force correlation function.