  We study the effects of the long-range disorder potential and warping on the
conductivity and mobility of graphene ribbons using the Landauer formalism and
the tight-binding p-orbital Hamiltonian. We demonstrate that as the length of
the structure increases the system undergoes a transition from the ballistic to
the diffusive regime. This is reflected in the calculated electron density
dependencies of the conductivity and the mobility. In particular, we show that
the mobility of graphene ribbons varies as mu(n) n^(-lambda), with
0<lambda<0.5. The exponent lambda depends on the length of the system with
lambda=0.5 corresponding to short structures in the ballistic regime, whereas
the diffusive regime lambda=0 (when the mobility is independent on the electron
density) is reached for sufficiently long structures. Our results can be used
for the interpretation of experimental data when the value of lambda can be
used to distinguish the transport regime of the system (i.e. ballistic,
quasi-ballistic or diffusive). Based on our findings we discuss available
experimental results.
