相关论文: Joint Singular Value Distribution of Two Correlate…

Given even strongly log-concave random vectors $X_{0}$ and $X_{1}$ in $\mathbb{R}^n$, we show that a natural joint distribution $(X_{0},X_{1})$ satisfies, \begin{equation} e^{ - \frac{1}{n}D ((1-t)X_{0} + t X_{1} \Vert Z)} \geq (1-t) e^{ -…

We discuss the non-self-averaging phenomena in the critical point of weakly disordered Ising ferromagnet. In terms of the renormalized replica Ginzburg-Landau Hamiltonian in dimensions D <4, we derive an explicit expression for the…

Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this work, we propose a solution to this problem by using a family of Rotation-based Iterative…

There exists an entire family of universal PDFs of the magnetization mode of the three dimensional Ising model parameterized by $\zeta = \lim_{L,\xi_{\infty}}L/\xi_{\infty}$ which is the ratio of the system size $L$ to the bulk correlation…

We study the one-point probability distribution function (PDF) for matter density averaged over spherical cells. The leading part to the PDF is defined by spherical collapse dynamics, whereas the next-to-leading part comes from the…

We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the…

In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…

We propose the exact calculation of the probability density function (PDF) and cumulative distribution function (CDF) of mutual information (MI) for a two-user MIMO MAC network over block Rayleigh fading channels. So far the PDF and CDF…

Intermittency in MHD turbulence has been analyzed using high resolution 2D numerical simulations. We show that the Probability Distribution Functions (PDFs) of the fluctuations of the Elsasser fields, magnetic field and velocity field…

Context: Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF). In order to successfully exploit such observables, a detailed…

The squared singular values of the product of $M$ complex Ginibre matrices form a biorthogonal ensemble, and thus their distribution is fully determined by a correlation kernel. The kernel permits a hard edge scaling to a form specified in…

The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the…

At any given scale, 3$\times$2-point statistics extract only three numbers from the joint distribution of the cosmic matter density and galaxy density fluctuations: their variances and their covariance. It is well known that the full shape…

Bivariate normal distributions are often used to describe the joint probability density of a pair of random variables. These distributions arise across many domains, from telecommunications, to meteorology, ballistics, and computational…

Parton distribution functions (PDFs) at large $x$ are poorly constrained by high-energy experimental data, but extremely important for probing physics beyond standard model at colliders. We study the calculation of PDFs at large-$x$ through…

We study matrix integrals of the form $$\int_{\mathrm{USp(2n)}}\prod_{j=1}^k\mathrm{tr}(U^j)^{a_j}\mathrm d U,$$ where $a_1,\ldots,a_r$ are natural numbers and integration is with respect to the Haar probability measure. We obtain a compact…

We revise the relation between Parton Distribution Functions (PDFs) and matrix elements computable from lattice QCD, focusing on the quasi-Parton Distribution Functions (qPDFs) approach. We exploit the relation between PDFs and qPDFs in the…

In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…

We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…

We derive a Fokker-Planck equation for joint probability density for an active particle coupled two heat reservoirs with harmonic, viscous, random forces. The approximate solution for the joint distribution density of all-to-all and three…