Related papers: Spectral properties of high dimensional rescaled s…
In this paper, we consider the separable covariance model, which plays an important role in wireless communications and spatio-temporal statistics and describes a process where the time correlation does not depend on the spatial location…
We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
We consider $n\times n$ random matrices $M_{n}=\sum_{\alpha =1}^{m}{\tau _{\alpha }}\mathbf{y}_{\alpha }\otimes \mathbf{y}_{\alpha }$, where $\tau _{\alpha }\in \mathbb{R}$, $\{\mathbf{y}_{\alpha }\}_{\alpha =1}^{m}$ are i.i.d. isotropic…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
Random Fisher matrices arise naturally in multivariate statistical analysis and understanding the properties of its eigenvalues is of primary importance for many hypothesis testing problems like testing the equality between two multivariate…
It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate…
For $k,m,n\in \mathbb{N}$, we consider $n^k\times n^k$ random matrices of the form $$ \mathcal{M}_{n,m,k}(\mathbf{y})=\sum_{\alpha=1}^m\tau_\alpha {Y_\alpha}Y_\alpha^T,\quad…
We study the universal properties of distributions of eigenvalues of random matrices in the large $N$ limit. The distributions fall in universality classes characterized entirely by the support of the spectral density.
We prove the existence of the limiting spectral distribution (LSD) of symmetric triangular patterned matrices and also establish the joint convergence of sequences of such matrices. For the particular case of the symmetric triangular Wigner…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…
This paper proposes a CLT for linear spectral statistics of random matrix $S^{-1}T$ for a general non-negative definite and {\bf non-random} Hermitian matrix $T$.
The existence of limiting spectral distribution (LSD) of $\hat{\Gamma}_u+\hat{\Gamma}_u^*$, the symmetric sum of the sample autocovariance matrix $\hat{\Gamma}_u$ of order $u$, is known when the observations are from an infinite dimensional…
We show that the variance of centred linear statistics of eigenvalues of GUE matrices remains bounded for large $n$ for some classes of test functions less regular than Lipschitz functions. This observation is suggested by the limiting form…
In this paper, we derive a unified method for establishing the distributional convergence of linear eigenvalue statistics (LES) for generalized patterned random matrices. We prove that for an $N \times N$ generalized patterned random matrix…
For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists…
Central limit theorems (CLTs) for high-dimensional random vectors with dimension possibly growing with the sample size have received a lot of attention in the recent times. Chernozhukov et al. (2017) proved a Berry--Esseen type result for…
In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the "general information-plus-noise" type, as studied in [14]. Through the equation defining its Stieltjes…