  We prove an invariance principle for a class of tilted (1+1)-dimensional SOS
models or, equivalently, for a class of tilted random walk bridges in Z_+. The
limiting objects are stationary reversible ergodic diffusions with drifts given
by the logarithmic derivatives of the ground states of associated singular
Sturm-Liouville operators. In the case of a linear area tilt, we recover the
Ferrari-Spohn diffusion with log-Airy drift, which was derived by Ferrari and
Spohn in the context of Brownian motions conditioned to stay above circular and
parabolic barriers.
