Related papers: Matrix variate and tensor variate Laplace distribu…
The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.
Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
This paper discusses the problem of symmetric tensor decomposition on a given variety $X$: decomposing a symmetric tensor into the sum of tensor powers of vectors contained in $X$. In this paper, we first study geometric and algebraic…
The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the…
We obtain variance inequalities for quadratic forms of weakly dependent random variables with bounded fourth moments. We also discuss two application. Namely, we use these inequalities for deriving the limiting spectral distribution of a…
Inspired from modern out-of-equilibrium statistical physics models, a matrix product based framework permits the formal definition of random vectors (and random time series) whose desired joint distributions are a priori prescribed. Its key…
We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these…
A new notion of displacement convexity on a matrix level is developed for density flows arising from mean-field games, compressible Euler equations, entropic interpolation, and semi-classical limits of non-linear Schr\"odinger equations.…
In this research paper, structured bi-matrix variate, matrix quadratic equations are considered. Some lemmas related to determining the eigenvalues of unknown matrices are proved. Also, a method of determining the diagonalizabe unknown…
We state and prove a classical version of the Laplace expansion theorem where all submatrices in the expansion are restricted to contain a specified common submatrix (CSM). The result states that (accounting for signs) this restricted…
A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a…
I present a short review of models for transverse-momentum distributions and transversity, with a particular attention on general features common to many models. I compare some model results with experimental extractions. I discuss the…
We define and study a family of distributions with domain complete Riemannian manifold. They are obtained by projection onto a fixed tangent space via the inverse exponential map. This construction is a popular choice in the literature for…
We establish an identity for E f (Y) -E f (X), when X and Y both have matrix variateskew-normal distributions and the function f fulfills some weak conditions. Thecharacteristic function of matrix variate skew normal distribution is then…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the…
The notion of a Laplace ladder for a discrete analogue of the Laplace equation is presented. The adjoint of the discrete Moutard equation and a discrete counterpart of the nonlinear form of Goursat equation are introduced.
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…