  We show that in generic isotropic holographic theories the longitudinal
Langevin diffusion coefficient along the string motion is larger compared to
that of the transverse direction. We argue that this is a universal relation
and we derive the generic conditions in order to be satisfied. A way to violate
the relation is to consider anisotropic gauge/gravity dualities. We give an
explicit example of this violation where the noise along the transverse
direction is larger than the noise occurring along the quark motion. Moreover,
we derive the effective world-sheet temperature for any generic theory and then
the conditions for negative excess noise. We argue that isotropic theories can
not have negative excess noise and we additionally remark that these conditions
are difficult to get satisfied, indicating positivity of the excess noise, even
in a large class of anisotropic holographic theories.
