  We formulate a random matrix-like model for the Polyakov loop in SU(N)
Yang-Mills theories. It describes a simplified dynamics in terms of eigenvalue
differences. The deconfinement phase transition encoded in center symmetry
breaking is reproduced including its nature being first order for SU(3) and
second order for SU(2). Analytical arguments about the phases are presented and
a comparison to other approaches is made.
