  Elucidating the nature of the glass transition has been the holy grail of
condensed matter physics and statistical mechanics for several decades. A
phenomenological aspect that makes glass formation a conceptually formidable
problem is that structural and dynamic correlations in glass-forming liquids
are too subtle to be captured at the level of conventional two-point functions.
As a consequence, a host of theoretical techniques, such as quenched amorphous
configurations of particles, have been devised and employed in simulations and
colloid experiments to gain insights into the mechanisms responsible for these
elusive correlations. Very often, though, the analysis of spatio-temporal
correlations is performed in the context of a single theoretical framework, and
critical comparisons of microscopic predictions of competing theories are
thereby lacking. Here, we address this issue by analysing the distribution of
localized excitations, which are building blocks of relaxation as per the
Dynamical Facilitation (DF) theory, in the presence of an amorphous wall, a
construct motivated by the Random First-Order Transition theory (RFOT). We
observe that spatial profiles of the concentration of excitations exhibit
complex features such as non-monotonicity and oscillations. Moreover, the
smoothly varying part of the concentration profile yields a length scale
$\xi_c$, which we compare with a previously computed length scale $\xi_{dyn}$.
Our results suggest a method to assess the role of dynamical facilitation in
governing structural relaxation in glass-forming liquids.
