  We propose a useful integral representation of the quenched free energy which
is applicable to any random systems. Our formula involves the generating
function of multi-boundary correlators, which can be interpreted on the bulk
gravity side as spacetime D-branes introduced by Marolf and Maxfield in
[arXiv:2002.08950]. As an example, we apply our formalism to the Airy limit of
the random matrix model and compute its quenched free energy under certain
approximations of the generating function of correlators. It turns out that the
resulting quenched free energy is a monotonically decreasing function of the
temperature, as expected.
