  We consider families of non-colliding random walks above a hard wall, which
are subject to a self-potential of tilted area type. We view such ensembles as
effective models for the level lines of a class of $2+1$-dimensional
discrete-height random surfaces in statistical mechanics. We prove that, under
rather general assumptions on the step distribution and on the self-potential,
such walks converge, under appropriate rescaling, to non-intersecting
Ferrari--Spohn diffusions associated with limiting Sturm--Liouville operators.
In particular, the limiting invariant measures are given by the squares of the
corresponding Slater determinants.
