  We study the density of states and localization properties of the lowest
Landau levels of graphene at high magnetic fields. We focus on the effects
caused by correlated long-range hopping disorder, which, in exfoliated
graphene, is induced by static ripples. We find that the broadening of the
lowest Landau level shrinks exponentially with increasing disorder correlation
length. At the same time, the broadening grows linearly with magnetic field and
with disorder amplitudes. The lowest Landau level peak shows a robust
splitting, whose origin we identify as the breaking of the sublattice (valley)
degeneracy.
