Related papers: Asymptotic Linear Spectral Statistics for Spiked H…
The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edges are independently drawn with probability depending on the locations of the two end…
We consider canonical determinantal random point processes with N particles on a compact Riemann surface X defined with respect to the constant curvature metric. In the higher genus (hyperbolic) cases these point processes may be defined in…
Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the…
The likelihood ratio test (LRT) is widely used for comparing the relative fit of nested latent variable models. Following Wilks' theorem, the LRT is conducted by comparing the LRT statistic with its asymptotic distribution under the…
For random matrices with block correlation structure we show that the fluctuations of linear eigenvalue statistics are Gaussian on all mesoscopic scales with universal variance which coincides with that of the Gaussian unitary or Gaussian…
Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…
Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…
We show that if a permutation statistic can be written as a linear combination of bivincular patterns, then its moments can be expressed as a linear combination of factorials with constant coefficients. This generalizes a result of…
Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…
We consider linear spectral statistics of the form $\mathrm{tr} ( \varphi (H))$ for test functions $\varphi$ of low regularity and Wigner matrices $H$ with smooth entry distribution. We show that for functions $\varphi$ in the Sobolev space…
The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings,…
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 develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…
The global clustering coefficient serves as a powerful metric for the structural analysis and comparison of complex networks. Random geometric graphs offer a realistic framework for representing the spatial constraints and geometry often…
The fits of 0.4 Ca(NO_3)_2 0.6 K(NO_3) (CKN) by schematic mode-coupling models [V. Krakoviack and C. Alba-Simionesco, J. Chem. Phys. 117, 2161-2171 (2002)] are analyzed by asymptotic expansions. The validity of both the power-law and the…
This paper deals with subspace estimation in the small sample size regime, where the number of samples is comparable in magnitude with the observation dimension. The traditional estimators, mostly based on the sample correlation matrix, are…
Consider a $N\times n$ matrix $\Sigma_n=\frac{1}{\sqrt{n}}R_n^{1/2}X_n$, where $R_n$ is a nonnegative definite Hermitian matrix and $X_n$ is a random matrix with i.i.d. real or complex standardized entries. The fluctuations of the linear…
We prove a central limit theorem (CLT) for the product of a class of random singular matrices related to a random Hill's equation studied by Adams$\unicode{x2013}$Bloch$\unicode{x2013}$Lagarias. The CLT features an explicit formula for the…
In this paper we show how to apply classical probabilistic tools for partial sums $\sum_{j=0}^{n-1}\varphi\circ\tau^j$ generated by a skew product $\tau$, built over a sufficiently well mixing base map and a random expanding dynamical…
The asymptotic mutual information (MI) analysis for multiple-input multiple-output (MIMO) systems over double-scattering channels has achieved engaging results, but the convergence rates of the mean, variance, and the distribution of the MI…