Slepian models for Gaussian Random Landscapes

TL;DR

This paper develops mathematical techniques to generate constrained Gaussian random landscapes, enabling the study of rare features like minima and inflection points relevant for scalar potential modeling.

Contribution

It introduces Slepian models for constrained realizations of Gaussian fields, providing analytical and numerical methods to explore low-probability landscape features.

Findings

Efficient generation of minima at arbitrary potential heights.

Calculation of non-perturbative decay rates for these minima.

Statistical analysis of inflationary inflection points within the models.

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.