  We apply the Kubo-Anderson stochastic theory of molecular spectral lineshape
to the case of polaritons formed in the collective strong coupling regime. We
investigate both the fast and slow limits of the random frequency modulation of
the emitter as well as the intermediate regime and show how the interplay
between the characteristic timescales of the cavity and the molecular disorder
is expressed in the observed polaritons lineshapes. The analytical solution
obtained for the slow limit is valid for any ratio between the inhomogeneous
broadening of the molecules and the Rabi splitting, especially relevant for
molecular polaritons where these two quantities can be of the same order of
magnitude.
