  Phenomenologically interesting scalar potentials are highly atypical in
generic random landscapes. We develop the mathematical techniques to generate
constrained random potentials, i.e. Slepian models, which can globally
represent low-probability realizations of the landscape. We give analytical as
well as numerical methods to construct these Slepian models for constrained
realizations of a full Gaussian random field around critical as well as
inflection points. We use these techniques to numerically generate in an
efficient way a large number of minima at arbitrary heights of the potential
and calculate their non-perturbative decay rate. Furthermore, we also
illustrate how to use these methods by obtaining statistical information about
the distribution of observables in an inflationary inflection point constructed
within these models.
