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Slepian models for Gaussian random landscapes. (English) Zbl 1437.85006

Summary: 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 [D. Slepian, in: Proc. Symp. Time Series Analysis, Brown Univ. 1962, 104–115 (1963; Zbl 0139.34101)], 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.

MSC:

85A40 Astrophysical cosmology
83F05 Relativistic cosmology
62P35 Applications of statistics to physics
60H40 White noise theory

Citations:

Zbl 0139.34101
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References:

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