Related papers: Singular Riesz measures on symmetric cones

In this paper, we introduce, for a multiplier $\chi$, a notion of generalized power function $x\mapsto \Delta_{\chi}(x),$ defined on the homogeneous cone ${\mathcal{P}}$ of a Vinberg algebra ${\mathcal{A}}$. We then extend to…

The superbosonisation identity of Littelmann-Sommers-Zirnbauer is a new tool to study universality of random matrix ensembles via supersymmetry, which is applicable to non-Gaussian invariant distributions. In this note, we identify the…

We introduce a compactification of the space of simple positive divisors on a Riemann surface, as well as a compactification of the universal family of punctured surfaces above this space. These are real manifolds with corners. We then…

The statistical duality of distributions is a powerful tool for statistical inferences. In the paper the statistical duality of Laplace distribution is discussed. As shown the confidence density of the parameter of this distribution is…

We show that any generalised smooth distribution on a smooth manifold, possibly of non-constant rank, admits a Riemannian metric. Using such a metric, we attach a Laplace operator to any smooth distribution as such. When the underlying…

This article derives the distribution of random matrix $\mathbf{X}$ associated with the transformation $\mathbf{Y} = \mathbf{X}^{*}\mathbf{X}$, such that $\mathbf{Y}$ has a Riesz distribution for real normed division algebras. Two versions…

The literature presents the characteristic function of the Wishart distribution on m times m matrices as an inverse power of the determinant of the Fourier variable, the exponent being the positive, real shape parameter. I demonstrate that…

We develop and use some key concepts of potential theory, such as balayage and duality between measures and their potentials, to study the distribution of masses of subharmonic functions while restrictions to their growth near the boundary…

From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…

In [8] we found a class of overlapping asymmetric self-similar measures on the real line, which are generically absolutely continuous with respect to the Lebesgue measure. Here we construct exceptional measures in this class being singular.

We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…

These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…

A measure independence property of Lebesgue measurable convex cones of $\mathbb{C}^2$, for $SU(2)$ transformations invariant continuous probability joint distributions over $\mathbb{C}^2$, will be proved using the existence of the Haar…

In recent years various results about locally symmetric manifolds were proven using probabilistic approaches. One of the approaches is to consider random manifolds by associating a probability measure to the space of discrete subgroups of…

We prove that for a certain class of $n$ dimensional rank one locally symmetric spaces, if $f \in L^p$, $1\leq p \leq 2$, then the Riesz means of order $z$ of $f$ converge to $f$ almost everywhere, for $\operatorname{Re}z> (n-1)(1/p-1/2).$

Based on a student research project this article gives a short review on Wishart processes. A Wishart procces is a matrix valued continuous time stochastic process with a marginal Wishart distribution. The Wishart distribution is a matrix…

This is the fourth article of our series. Here, we study weighted norm inequalities for the Riesz transform of the Laplace-Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume…

Let $E\subset \mathbb{R}^{n+1}$, $n\ge 2$, be an Ahlfors-David regular set of dimension $n$. We show that the weak-$A_\infty$ property of harmonic measure, for the open set $\Omega:= \mathbb{R}^{n+1}\setminus E$, implies uniform…

Let $\gamma_{-1}$ be the absolutely continuous measure on $\mathbb{R}^n$ whose density is the reciprocal of a Gaussian and consider the natural weighted Laplacian $\mathcal{A}$ on $L^2(\gamma_{-1})$. In this paper, we prove boundedness and…

A new class of dependent random measures which we call {\it compound random measures} are proposed and the use of normalized versions of these random measures as priors in Bayesian nonparametric mixture models is considered. Their…