  We study two-point correlation function in a medium composed of two kinds of
matter, which is the dual of a three-dimensional generalized $p$-brane gas
geometry. Following the holographic prescription, we calculate temporal and
spatial two-point functions in the medium. In general, the screening effect of
the medium makes two-point functions decrease more rapidly than the CFT's
two-point function. In the extremal limit, however, we find that a temporal
two-point function is still conformal. This indicates that a two-dimensional UV
CFT flows into a one-dimensional quantum mechanics in the IR limit. This is
consistent with the fact that the near horizon geometry in the extremal limit
reduces to AdS$_2$. We also investigate holographic mutual information
representing the correlation between two subsystems. We show that a critical
distance in the IR region, where the mutual information vanishes, leads to a
similar behavior to the correlation length of a two-point function.
