Related papers: Gaussian vectors with Markov property

Structure formation in our Universe creates non-Gaussian random fields that will soon be observed over almost the entire sky by the Euclid satellite, the Vera-Rubin observatory, and the Square Kilometre Array. An unsolved problem is how to…

We discuss the application of random projections to the fundamental problem of deciding whether a given point in a Euclidean space belongs to a given set. We show that, under a number of different assumptions, the feasibility and…

We study geodesically convex (g-convex) problems that can be written as a difference of Euclidean convex functions. This structure arises in several optimization problems in statistics and machine learning, e.g., for matrix scaling,…

In the work a characterization of difference of multivariate Gaussian measures is found on the family of centered Eucledian balls. In particular, it helps to bound corresponding Kolmogorov distance.

We introduce a new definition of exponential family of Markov chains, and show that many characteristic properties of the usual exponential family of probability distributions are properly extended to Markov chains. The method of…

We argue that the mathematical structure, enabling certain cascading and emergent phenomena to intuitively emerge, coincides with Galois connections. We introduce the notion of generative effects to formally capture such phenomena. We…

We use Herbrand's theorem to give a new proof that Euclid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a…

We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the…

We consider quadratic forms of deterministic matrices $A$ evaluated at the random eigenvectors of a large $N \times N$ GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove…

We investigate Gauss maps of (not necessarily normal) projective toric varieties over an algebraically closed field of arbitrary characteristic. The main results are as follows: (1) The structure of the Gauss map of a toric variety is…

We show that the quantum Hamilton Jacobi approach to a class of quantum mechanical bound state problems and the Gaussian orthogonal ensemble of random matrix theory are equivalent. The Berry connection for both problems is identical to…

We derive the Wick theorem for the q-Exponential distribution. We use the theorem to derive an algorithm for finding parameters of the correlation matrix of q-Exponentialy distributed random variables given empirical spectral moments of the…

We consider the problem of estimating the mean $f$ of a Gaussian vector $Y$ with independent components of common unknown variance $\sigma^{2}$. Our estimation procedure is based on estimator selection. More precisely, we start with an…

Many authors have studied the phenomenon of typically Gaussian marginals of high-dimensional random vectors; e.g., for a probability measure on $\R^d$, under mild conditions, most one-dimensional marginals are approximately Gaussian if $d$…

We study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose…

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

We study the Gromov-Hausdorff convergence of metric pairs and metric tuples and prove the equivalence of different natural definitions of this concept. We also prove embedding, completeness and compactness theorems in this setting. Finally,…

We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…

This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by…

Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean…