Slepian models for Gaussian Random Landscapes
  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.
