Related papers: Covariance of centered distributions on manifold

Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…

We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…

The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…

We consider Riemannian $n$-manifolds $M$ with nontrivial $\kappa$-nullity "distribution" of the curvature tensor $R$, namely, the variable rank distribution of tangent subspaces to $M$ where $R$ coincides with the curvature tensor of a…

Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational…

We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sum of derivatives of generalized lattice…

A new family of multivariate distributions, which shall be termed multivector variate distributions, based in the family of the multivariate contoured elliptically distribution is proposed. Several particular cases of multivector variate…

In the recent articles \cite{PSU1,PSU3}, a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central concept is the…

Various metrics for comparing diffusion tensors have been recently proposed in the literature. We consider a broad family of metrics which is indexed by a single power parameter. A likelihood-based procedure is developed for choosing the…

Distributional tensor fields can be regarded as multilinear mappings with distributional values or as (classical) tensor fields with distributional coefficients. We show that the corresponding isomorphisms hold also in the bornological…

We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…

Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of…

Tensor distributions and their derivatives are described without assuming the presence of a metric. This provides a natural framework for discussing tensor distributions on manifolds with degenerate metrics, including in particular metrics…

On a Riemannian or a semi-Riemannian manifold, the metric determines invariants like the Levi-Civita connection and the Riemann curvature. If the metric becomes degenerate (as in singular semi-Riemannian geometry), these constructions no…

We establish a full classification of degree $2$ codimension one distributions on $\mathbb{P}^3$ according to invariants of their tangent sheaves.

In Riemann geometry, the relations among two transversal submanifolds and global manifold are discussed. By replacing the normal vector of a submanifold with the tangent vector of another submanifold, the metric tensors, Christoffel symbols…

In this paper we continue our recent study of a manifold endowed with a singular or regular distribution, determined as the image of the tangent bundle under a smooth endomorphism, and generalize Bochner's technique to the case of a…

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…

Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…