English
Related papers

Related papers: A note on some extensions of the matrix angular ce…

200 papers

Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…

Statistical Mechanics · Physics 2013-05-29 Carsten Timm

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,…

Probability · Mathematics 2021-01-19 Cosme Louart , Romain Couillet

In this paper, the study of bivariate generalised beta type I and II distributions is extended to the complex matrix variate case, for which the corresponding density functions are found. In addition, for complex bimatrix variate beta type…

Statistics Theory · Mathematics 2009-06-08 Jose A. Diaz-Garcia , Ramon Gutierrez-Jaimez

This paper proposes the density and characteristic functions of a general matrix quadratic form $\mathbf{X}^{*}\mathbf{AX}$, when $\mathbf{A} = \mathbf{A}^{*}$, $\mathbf{X}$ has a matrix multivariate elliptical distribution and…

Statistics Theory · Mathematics 2012-10-22 Jose A. Diaz-Garcia

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4)…

Statistical Mechanics · Physics 2015-05-14 Satya N. Majumdar , Celine Nadal , Antonello Scardicchio , Pierpaolo Vivo

The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…

Fluid Dynamics · Physics 2013-10-16 H. Mouri

Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys…

The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate…

Mesoscale and Nanoscale Physics · Physics 2009-10-30 M. C. W. van Rossum , Igor V. Lerner , Boris L. Altshuler , Th. M. Nieuwenhuizen

We consider the problem of determining the limiting spectral distribution for random matrices whose row distributions are permitted to have limited dependence. We assume mild moment conditions and give an extension of the…

Probability · Mathematics 2018-01-16 Chris Connell , Pawan Patel

This paper is a brief review of recent developments in random matrix theory. Two aspects are emphasized: the underlying role of integrable systems and the occurrence of the distribution functions of random matrix theory in diverse areas of…

Mathematical Physics · Physics 2007-05-23 Craig A. Tracy , Harold Widom

We review the formalism of center-of-mass tomograms that allows us to describe quantum states in terms of probability distribution functions. We introduce the concept of separable and entangled probability distributions for the…

Quantum Physics · Physics 2024-06-12 Ivan V. Dudinets , Margarita A. Man'ko , Vladimir I. Man'ko

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…

Probability · Mathematics 2014-08-06 Anirban Basak , Arup Bose , Soumendu Sundar Mukherjee

The investigation of the orientation of galaxies is a standard test concerning to scenarios of galaxy formation, because different theories of galaxy formation make various predictions regarding to the angular momentum of galaxies. The new…

Astrophysics of Galaxies · Physics 2014-04-02 Elena Panko , Paulina Piwowarska , Jolanta Godlowska , Wlodzimierz Godlowski , Piotr Flin

In this paper it is shown that a generalized circulant matrix underlies every weakly Coupled Map Lattice (CML), independently of the form of the coupling term. Therefore, this matrix will appear always perturbative methods are used to get…

Pattern Formation and Solitons · Physics 2009-03-25 M. Dolores Sotelo Herrera Jesus San Martin

We consider a versatile matrix model of the form ${\bf A}+i {\bf B}$, where ${\bf A}$ and ${\bf B}$ are real random circulant matrices with independent but, in general, nonidentically distributed Gaussian entries. For this model, we derive…

Mathematical Physics · Physics 2025-04-29 Sunidhi Sen , Himanshu Shekhar , Santosh Kumar

We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…

Methodology · Statistics 2022-06-07 Andrew J. Cron , Mike West

A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the…

Nuclear Theory · Physics 2009-10-31 M. S. Hussein , M. P. Pato

Cluster-Weighted Modeling (CWM) is a flexible mixture approach for modeling the joint probability of data coming from a heterogeneous population as a weighted sum of the products of marginal distributions and conditional distributions. In…

Methodology · Statistics 2012-12-20 Salvatore Ingrassia , Simona C. Minotti , Antonio Punzo , Giorgio Vittadini

This paper is continuation of the systematic study of distribution of quadrant marked mesh patterns. We study quadrant marked mesh patterns on up-down and down-up permutations, also known as alternating and reverse alternating permutations,…

Combinatorics · Mathematics 2012-05-04 Sergey Kitaev , Jeffrey Remmel

Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…

Statistics Theory · Mathematics 2020-05-15 Sharon X. Lee , Geoffrey J. McLachlan