Related papers: A generalised Kotz type distribution and Riesz dis…
We consider an indexed class of real symmetric random matrices which generalize the symmetric Hankel and Reverse Circulant matrices. We show that the limiting spectral distributions of these matrices exist almost surely and the limit is…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
We introduce and analyze spaces and algebras of generalized functions which correspond to H\" older, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are…
We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone. We give a general formula for moments of the…
A concise derivation of a new multiplicative product of Schwartz distributions is presented. The new product $\star$ is defined in the vector space ${\cal A}$ of piecewise smooth functions on $\bkR$ and all their (distributional)…
This is an introductory note concerning the distribution vectors in a unitary representation of a Lie group. We discuss the definition of matrix coefficients associated with a pair of distributions and how one can compute them. Most of the…
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…
We give a formula for the tail of the distribution of the non-commutative Rademacher series, which generalizes the result that is already available in the commutative case. As a result, we are able to calculate the norm of these series in…
Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…
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 will study the relationship between two well-known theories, genetic evolution and random matrix theory in the context of many-body systems. It is suggested that genetic evolution can be described by a random matrix theory with…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
We present a method for mapping variations between probability distribution functions and apply this method within the context of measuring galaxy redshift distributions from imaging survey data. This method, which we name PITPZ for the…
This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…
We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed random vectors, combining mean and extreme behaviors. It extends the so-called 'normex' approach from a univariate to a multivariate framework. We…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…
Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of positive-definite matrices (here called covariance…
Kaczmarz's alternating projection method has been widely used for solving a consistent (mostly over-determined) linear system of equations Ax=b. Because of its simple iterative nature with light computation, this method was successfully…
We propose an interpretation of previous experimental and numerical experiments, showing that for a large class of systems, distributions of global quantities are similar to a distribution originally obtained for the magnetization in the…