Abstract
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.
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Blanco-Pillado, J.J., Sousa, K. & Urkiola, M.A. Slepian models for Gaussian random landscapes. J. High Energ. Phys. 2020, 142 (2020). https://doi.org/10.1007/JHEP05(2020)142
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DOI: https://doi.org/10.1007/JHEP05(2020)142