Interestingly, the rectangular distribution takes on a completely new character, now exhibiting outward-facing spectral features at lower disorders (i.e., increasing the Rabi splitting when 0 < σ / Ã0 < 5). Of the three distributions, the rectangular distribution contains the largest average probability den- A 0 = 0.01 a.u., ω c = 1.00 a.u., N r = 50, 000, N cheb = 2500, γ = 0.001 a.u. Note that the data shown here is identical to Fig. except that the intensity is on a log scale. sity, ⟨P R ⟩ E > ⟨P G ⟩ E ≈ ⟨P L ⟩ E (see Eq. . For the case of N = 1 or N = 2, we hypothesize that the molecular distribution for a given stochastic configuration cannot wellenforce the hard boundaries at E = ω c ± σ 2 . While for N = 100, the hard boundaries are evident for most statistical samples in the average, allowing for the formation of polaritons which also exhibit the features dictated by such hard bound-aries. Such features were also discussed in Ref. , where the authors analyzed the same excitation frequency distributions using a large-N expansion of the problem and extracting the analytic molecular susceptibility χ(E). This is also discussed in the recent work using perturbation theory analysis and response function based simulations of the linear absorption spectra. Notably, our results at N = 100 match the features predicted by the large-N analytical theory in Ref. .