  We investigate puncture statistics based on the covariant area spectrum in
loop quantum gravity. First, we consider Maxwell-Boltzmann statistics with a
Gibbs factor for punctures. We establish formulae which relate physical
quantities such as horizon area to the parameter characterizing holographic
degrees of freedom. We also perform numerical calculations and obtain
consistency with these formulae. These results tell us that the holographic
bound is satisfied in the large area limit and correction term of the
entropy-area law can be proportional to the logarithm of the horizon area.
Second, we also consider Bose-Einstein statistics and show that the above
formulae are also useful in this case. By applying the formulae, we can
understand intrinsic features of Bose-Einstein condensate which corresponds to
the case when the horizon area almost consists of punctures in the ground
state. When this phenomena occurs, the area is approximately constant against
the parameter characterizing the temperature. When this phenomena is broken,
the area shows rapid increase which suggests the phase transition from quantum
to classical area.
