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We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using Berry's conjecture, we calculate the peak height distributions and the correlation functions. We demonstrate that the corrections to the…
The conjectured three generic local bulk statistics amongst all non-Hermitian random matrix symmetry classes have recently been extended to three generic local edge statistics. We study analytically and numerically complex spacing ratios…
Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing…
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex…
The exploration of associations between random objects with complex geometric structures has catalyzed the development of various novel statistical tests encompassing distance-based and kernel-based statistics. These methods have various…
We show that the fluctuations of the linear eigenvalue statistics of a non-Hermitian random band matrix of increasing bandwidth $b_{n}$ with a continuous variance profile $w_{\nu}(x)$ converges to a $N(0,\sigma_{f}^{2}(\nu))$, where…
In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…
As an important topic in Mathematical Physics and statistics, random matrices theory has found uses in many aspects of modern physics and multivariate analysis. This paper is to investigate the Gaussian fluctuations for linear spectral…
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…
Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate…
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…
The main theme of this paper is a modification of the likelihood ratio test (LRT) for testing high dimensional covariance matrix. Recently, the correct asymptotic distribution of the LRT for a large-dimensional case (the case $p/n$…
In this paper we use a probabilistic approach to derive the expressions for the characteristic functions of basic statistics defined on permutation tableaux. Since our expressions are exact, we can identify the distributions of basic…
Consider large signal-plus-noise data matrices of the form $S + \Sigma^{1/2} X$, where $S$ is a low-rank deterministic signal matrix and the noise covariance matrix $\Sigma$ can be anisotropic. We establish the asymptotic joint distribution…
We prove a central limit theorem (CLT) for the Frechet mean of independent and identically distributed observations in a compact Riemannian manifold assuming that the population Frechet mean is unique. Previous general CLT results in this…
In clinical trials, studies often present longitudinal data or clustered data. These studies are commonly analyzed using linear mixed models (LMMs), usually considering Gaussian assumptions for random effect and error terms. Recently,…
We investigate the spectral properties of the Dirichlet Laplacian on large finite metric balls within irregular infinite graphs of quadratic volume growth. We consider an exhaustion $G_n = B_{R_n}(x_0)$ and the spectral zeta value $Z_n(1) =…
Recent theoretical works have characterized the dynamics of wide shallow neural networks trained via gradient descent in an asymptotic mean-field limit when the width tends towards infinity. At initialization, the random sampling of the…