  The density of states near zero energy in a graphene due to strong point
defects with random positions are computed. Instead of focusing on density of
states directly, we analyze eigenfunctions of inverse T-matrix in the unitary
limit. Based on numerical simulations, we find that the squared magnitudes of
eigenfunctions for the inverse T-matrix show random-walk behavior on defect
positions. As a result, squared magnitudes of eigenfunctions have equal {\it a
priori} probabilities, which further implies that the density of states is
characterized by the well-known Thomas-Porter type distribution. The numerical
findings of Thomas-Porter type distribution is further derived in the
saddle-point limit of the corresponding replica field theory of inverse
T-matrix. Furthermore, the influences of the Thomas-Porter distribution on
magnetic and transport properties of a graphene, due to its divergence near
zero energy, are also examined.
