  We consider an effect of weak impurities on electronic properties of graphene
within the functional renormalization-group approach. The energy dependences of
the electronic self-energy and density of states near the neutrality point are
discussed. Depending on the symmetry of the impurities, the electronic damping
$\Gamma$ and density of states $\rho$ can deviate substantially from those
given by the self-consistent Born approximation. We investigate the crossover
from the results of the self-consistent Born approximation, which are valid far
from the neutrality point to the strong-coupling (diffusive) regime near the
neutrality point. For impurities, which are diagonal in both, valley and
sublattice indices, we obtain finite density of states at the Fermi level with
the values, which are much bigger than the results of the self-consistent Born
approximation.
