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

The Polyakov loop models in the large N limit: Correlation function and screening masses