  The surface-brightness profiles of galaxies are well described by the
S\'ersic law: systems with high S\'ersic index m have steep central profiles
and shallow outer profiles, while systems with low m have shallow central
profiles and steep outer profiles. R. Cen (2014, ApJL, 790, L24) has
conjectured that these profiles arise naturally in the standard cosmological
model with initial density fluctuations represented by a Gaussian random field
(GRF). We explore and confirm this hypothesis with N-body simulations of
dissipationless collapses in which the initial conditions are generated from
GRFs with different power spectra. The numerical results show that GRFs with
more power on small scales lead to systems with higher m. In our purely
dissipationless simulations the S\'ersic index is in the range 2<m<6.5. It
follows that systems with S\'ersic index as low as m=2 can be produced by
coherent dissipationless collapse, while high-m systems can be obtained if the
assembly history is characterized by several mergers. As expected, dissipative
processes appear to be required to obtain exponential profiles (m=1).
