Related papers: Random Matrices and U-Statistics

We consider the complex eigenvalues of a Wishart type random matrix model $X=X_1 X_2^*$, where two rectangular complex Ginibre matrices $X_{1,2}$ of size $N\times (N+\nu)$ are correlated through a non-Hermiticity parameter $\tau\in[0,1]$.…

We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index beta=1,2 and 4. Our generalised model has a fat-tailed distribution while preserving the invariance…

This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

The family of U-statistics plays a fundamental role in statistics. This paper proves a novel exponential inequality for U-statistics under the time series setting. Explicit mixing conditions are given for guaranteeing fast convergence, the…

We discuss the applications of Random Matrix Theory in the context of financial markets and econometric models, a topic about which a considerable number of papers have been devoted to in the last decade. This mini-review is intended to…

I propose two U-statistics to test coefficients in generalized linear models. One of them is used to deal with global hypothesis and the other one to test with the nuisance parameter. Both the statistics proposed are within high-dimensional…

We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results…

We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…

We consider random stochastic matrices $M$ with elements given by $M_{ij}=|U_{ij}|^2$, with $U$ being uniformly distributed on one of the classical compact Lie groups or associated symmetric spaces. We observe numerically that, for large…

We present applications of statistical data analysis methods from both bi- and multivariate statistics to find suitable sets of neutron star features that can be leveraged for accurate and EoS independent -- or universal -- relations. To…

A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…

Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier work has exhibited a parametrisation of the corresponding Cholesky factorisation in terms of partial…

We study the universality of the eigenvalue statistics of the covariance matrices $\frac{1}{n}M^* M$ where $M$ is a large $p\times n$ matrix obeying condition $\bf{C1}$. In particular, as an application, we prove a variant of universality…

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…

We derive a new representation for $U$- and $V$-statistics. Using this representation, the asymptotic distribution of $U$- and $V$-statistics can be derived by a direct application of the Continuous Mapping theorem. That novel approach not…

A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…

It is known that the empirical spectral distribution of random matrices obtained from linear codes of increasing length converges to the well-known Marchenko-Pastur law, if the Hamming distance of the dual codes is at least 5. In this…

In this paper we study the local law for eigenvalues of large random regular bipartite graphs with degree growing arbitrarily fast. We prove that the empirical spectral distribution of the adjacency matrix converges to a scaled down copy of…

Determinantal Point Processes (DPPs), which originate from quantum and statistical physics, are known for modelling diversity. Recent research [Ghosh and Rigollet (2020)] has demonstrated that certain matrix-valued $U$-statistics (that are…