  The Dirac fermion in the random chiral models is studied which includes the
random gauge field model and the random hopping model. We focus on a connection
between continuum and lattice models to give a clear perspective for the random
chiral models. Two distinct structures of density of states (DoS) around zero
energy, one is a power-law dependence on energy in the intermediate energy
range and the other is a diverging one at zero energy, are revealed by an
extensive numerical study for large systems up to $250\times 250$. For the
random hopping model, our finding of the diverging DoS within very narrow
energy range reconciles previous inconsistencies between the lattice and the
continuum models.
