  The stationary measures of the Kardar-Parisi-Zhang equation on an interval
have been computed recently. We present a rather direct derivation of this
result by taking the weak asymmetry limit of the matrix product ansatz for the
asymmetric simple exclusion process. We rely on the matrix product ansatz
representation of Enaud and Derrida, which allows to express the steady-state
in terms of re-weighted simple random walks. In the continuum limit, its
measure becomes a path integral (or re-weighted Brownian motion) of the form
encountered in Liouville quantum mechanics, recovering the recent formula.
