  We explore the 't Hooft-Veneziano limit of the Polyakov loop models at finite
baryon chemical potential. Using methods developed by us earlier we calculate
the two- and $N$-point correlation functions of the Polyakov loops. This gives
a possibility to compute the various potentials in the confinement phase and to
derive the screening masses outside the confinement region. In particular, we
establish the existence of complex masses and an oscillating decay of
correlations in a certain range of parameters. Furthermore, it is shown that
the calculation of the $N$-point correlation function in the confinement phase
reduces to the geometric median problem. This leads to a large $N$ analog of
the $Y$ law for the baryon potential.
