Related papers: Operator Regular Variation of Multivariate Liouvil…
We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary…
In this paper, we consider the problem of order preservation under addition and multiplication operators over the vector space of univariate real-valued random variables. Consistent with the case of usual order over the real numbers-as…
We analyze the average behavior of various arithmetic functions at the values of degree $d$ binary forms ordered by height, with probability $1$. This approach yields averaged versions of the Chowla conjecture and the Bateman-Horn…
Polynomials in differentiation operators are considered. The Darboux transformations covariance determines non-Abelian entries to form the coefficients of the polynomials. Joint covariance of a pair of such polynomials (Lax pair) as a…
A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of…
We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series…
The evolution of mixed states of a closed quantum system is described by a group of evolution superoperators whose infinitesimal generator (the quantum Liouville superoperator, or Liouvillian) determines the mixed-state counterpart of the…
We consider the iteration of a unitary operator on a separable Hilbert space and study the spreading rates of the associated discrete-time dynamical system relative to a given orthonormal basis. We prove lower bounds for the transport…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
In this paper, we construct operator fractional L\'evy motion (ofLm), a broad class of non-Gaussian stochastic processes that are covariance operator self-similar, have wide-sense stationary increments and display infinitely divisible…
Distributed formation maneuver control refers to the problem of maneuvering a group of agents to change their formation shape by adjusting the motions of partial agents, where the controller of each agent only requires local information…
We study the tail bound of the emperical covariance of multivariate normal distribution. Following the work of (Gittens & Tropp, 2011), we provide a tail bound with a small constant.
We use the "Value Distribution" theory developed by Pearson and Breimesser to obtain a sequence of functions in the eigenvalue parameter for some Sturm-Liouville problems which have the property of being "uniformly asymptotically…
Liouville copulas, which were introduced in McNeil and Neslehova (2010), are asymmetric generalizations of the ubiquitous Archimedean copula class. They are the dependence structures of scale mixtures of Dirichlet distributions, also called…
We introduce some new indexes to measure the departure of any multivariate continuous distribution on non-negative orthant from a given reference one such the uncorrelated exponential model, similar to the relative Fisher dispersion indexes…
We give an alternative proof of the general chain rule for functions of bounded variation ([ADM90]), which allows to compute the distributional differential of $\varphi\circ F$, where $\varphi\in \mathrm{LIP}(\mathbb{R}^m)$ and…
We introduce the notion of symmetric covariation, which is a new measure of dependence between two components of a symmetric $\alpha$-stable random vector, where the stability parameter $\alpha$ measures the heavy-tailedness of its…
We revisit multivariate extreme value theory modeling by emphasizing multivariate regular variations and the multivariate Breiman Lemma. This allows us to recover in a simple framework the most popular multivariate extreme value…
In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential…