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In random matrix theory (RMT), the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian…

Statistical Mechanics · Physics 2009-11-13 O. Bohigas , J. X. de Carvalho , M. P. Pato

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

Methodology · Statistics 2025-06-12 Tongyu Li , Fang Yao , Anru R. Zhang

M-eigenvalues of fourth order hierarchically symmetric tensors play a significant role in nonlinear elastic material analysis and quantum entanglement problems. This paper focuses on computing extreme M-eigenvalues for such tensors. To…

Optimization and Control · Mathematics 2026-02-03 Zhuolin Du , Yisheng Song

High-dimensional tensor-valued data have recently gained attention from researchers in economics and finance. We consider the estimation and inference of high-dimensional tensor factor models, where each dimension of the tensor diverges.…

Methodology · Statistics 2025-09-30 Bin Chen , Yuefeng Han , Qiyang Yu

The Poisson-binomial distribution is useful in many applied problems in engineering, actuarial science, and data mining. The Poisson-binomial distribution models the distribution of the sum of independent but not identically distributed…

Computation · Statistics 2017-02-07 Man Zhang , Yili Hong , Narayanaswamy Balakrishnan

The Rosenblatt distribution plays a key role in the limit theorems for non-linear functionals of stationary Gaussian processes with long-range dependence. We derive new expressions for the characteristic function of the Rosenblatt…

Statistics Theory · Mathematics 2025-07-01 Nikolai N. Leonenko , Andrey Pepelyshev

The Nearest Neighbour Spacing (NNS) distribution can be computed for generalized symmetric 2x2 matrices having different variances in the diagonal and in the off-diagonal elements. Tuning the relative value of the variances we show that the…

Chaotic Dynamics · Physics 2022-01-12 Adway Kumar Das , Anandamohan Ghosh

In this paper, we present an equitable partition theorem of tensors, which gives the relations between $H$-eigenvalues of a tensor and its quotient equitable tensor and extends the equitable partitions of graphs to hypergraphs. Furthermore,…

Combinatorics · Mathematics 2018-09-18 Ya-Lei Jin , Jie Zhang , Xiao-Dong Zhang

We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the "population spectrum"), given access to samples drawn from the…

Machine Learning · Computer Science 2017-07-18 Weihao Kong , Gregory Valiant

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…

Statistical Mechanics · Physics 2011-06-28 Z. Burda , A. Jarosz , G. Livan , M. A. Nowak , A. Swiech

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…

Statistics Theory · Mathematics 2022-08-04 Taras Bodnar , Dmitry Otryakhin , Erik Thorsen

A random vector $\bx\in \R^n$ is a vector whose coordinates are all random variables. A random vector is called a Gaussian vector if it follows Gaussian distribution. These terminology can also be extended to a random (Gaussian) matrix and…

Probability · Mathematics 2020-07-28 Yan Feng , Shan Song , Changqing Xu

We develop statistical models for samples of distribution-valued stochastic processes featuring time-indexed univariate distributions, with emphasis on functional principal component analysis. The proposed model presents an intrinsic rather…

Methodology · Statistics 2024-06-21 Hang Zhou , Hans-Georg Müller

Assume that f is a strict convex function with a unique minimum in R^n. We divide the vector of n-variables to d groups of vector subvariables with d at least two. We assume that we can find the partial minimum of f with respect to each…

Optimization and Control · Mathematics 2019-06-06 Shmuel Friedland

We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…

Mathematical Physics · Physics 2013-02-13 Sudhir R. Jain , Shashi C. L. Srivastava

In this paper we propose and analyze a virtual element method for the two dimensional non-symmetric diffusion-convection eigenvalue problem in order to derive a priori and a posteriori error estimates. Under the classic assumptions of the…

Numerical Analysis · Mathematics 2023-09-29 Danilo Amigo , Felipe Lepe , Gonzalo Rivera

Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…

Mathematical Physics · Physics 2013-10-21 Tim Wirtz , Thomas Guhr

A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussian entries leads to statistical quantities…

Classical Analysis and ODEs · Mathematics 2009-11-11 P. J. Forrester , N. S. Witte

We study the problem of estimating E(g(X)), where g is a real-valued function of d variables and X is a d-dimensional Gaussian vector with a given covariance matrix. We present a new unbiased estimator for E(g(X)) that combines the…

Statistics Theory · Mathematics 2023-04-18 Nabil Kahale

We consider (robust) inference in the context of a factor model for tensor-valued sequences. We study the consistency of the estimated common factors and loadings space when using estimators based on minimising quadratic loss functions.…

Methodology · Statistics 2023-08-29 Matteo Barigozzi , Yong He , Lingxiao Li , Lorenzo Trapani