  Polyakov loop eigenvalues and their N-dependence are studied in 2 and 4
dimensional SU(N) YM theory. The connected correlation function of the single
eigenvalue distributions of two separated Polyakov loops in 2D YM is calculated
and is found to have a structure differing from the one of corresponding
hermitian random matrix ensembles. No large $N$ non-analyticities are found for
two point functions in the confining regime. Suggestions are made for
situations in which large-N phase transitions involving Polyakov loops might
occur.
