  For Laplacian models in dimension $(1+1)$ we derive sample path large
deviations for the profile height function, that is, we study scaling limits of
Gaussian integrated random walks and Gaussian integrated random walk bridges
perturbed by an attractive force towards the zero-level, called pinning. We
study in particular the regime when the rate functions of the corresponding
large deviation principles admit more than one minimiser, in our models either
two, three, or five minimiser depending on the pinning strength and the
boundary conditions. This study complements corresponding large deviation
results for gradient systems with pinning for Gaussian random walk bridges in $
(1+1) $-dimension (\cite{FS04}) and in $(1+d) $-dimension (\cite{BFO}), and
recently in higher dimensions in \cite{BCF}. In particular it turns out that
the Laplacian cases, i.e., integrated random walks, show richer and more
complex structures of the minimiser of the rate functions which are linked to
different phases.
