Related papers: Slepian models for Gaussian Random Landscapes
We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…
We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We…
Landscape cosmology posits the existence of a convoluted, multidimensional, scalar potential -- the "landscape" -- with vast numbers of metastable minima. Random matrices and random functions in many dimensions provide toy models of the…
Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is…
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
The independent interval approximation of the excursion time distributions for Gaussian processes has been used in physics and engineering. A new but related approach matches the expected value of the clipped Slepian to the expected value…
We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy…
Random, multifield functions can set generic expectations for landscape-style cosmologies. We consider the inflationary implications of a landscape defined by a Gaussian random function, which is perhaps the simplest such scenario. Many key…
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…
The recently proposed non-Gaussian Mat\'{e}rn random field models, generated through Stochastic Partial differential equations (SPDEs), are extended by considering the class of Generalized Hyperbolic processes as noise forcings. The models…
The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an…
A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…
In this paper we will consider the problem of the numerical simulation of non-Gaussian, scalar random fields with a prescribed correlation structure provided either by a theoretical model or computed on a set of observational data.…
We discuss recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(>>1)-dimensional Gaussian landscape. The particular attention is paid to the case of landscapes with…
We propose a novel discrete method of constructing Gaussian Random Fields (GRF) based on a combination of modified spectral representations, Fourier and Blob. The method is intended for Direct Numerical Simulations of the V-Langevin…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
Gaussian Schell-model fields are examples of spatially partially coherent fields, which in recent years have found several unique applications. The existing techniques for generating Gaussian Schell-model (GSM) fields are based on…
Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…
The construction of effective and informative landscapes for stochastic dynamical systems has proven a long-standing and complex problem. In many situations, the dynamics may be described by a Langevin equation while constructing a…