Related papers: Local Central Limit Theorem for Determinantal Poin…

We show that the central limit theorem for linear statistics over determinantal point processes with $J$-Hermitian kernels holds under fairly general conditions. In particular, We establish Gaussian limit for linear statistics over…

We prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the…

We prove the central limit theorem (CLT) for a sequence of independent zero-mean random variables $\xi_j$, perturbed by predictable multiplicative factors $\lambda_j$ with values in intervals $[\underline\lambda_j,\overline\lambda_j]$. It…

Let $G$ be an $N \times N$ real matrix whose entries are independent identically distributed standard normal random variables $G_{ij} \sim \mathcal{N}(0,1)$. The eigenvalues of such matrices are known to form a two-component system…

We consider a random walk $(Y_N)_{N\geq 0}$ on $\mathbb{R}^2$ generated by successively applying independent random isometries, drawn from a fixed measure $\mu$, to the point $0$. When the support of $\mu$ is finite and includes an…

We consider the asymptotic normalcy of families of random variables $X$ which count the number of occupied sites in some large set. We write $Prob(X=m)=p_mz_0^m/P(z_0)$, where $P(z)$ is the generating function $P(z)=\sum_{j=0}^{N}p_jz^j$…

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 matrices from the elliptic Ginibre orthogonal ensemble (GinOE) are a certain linear combination of a real symmetric, and real anti-symmetric, real Gaussian random matrices and controlled by a parameter $\tau$. Our interest is in the…

It is well-known that, on a purely algebraic level, a simplified algebraic version of the Central Limit Theorem (CLT) can be proved in the framework of a noncommutative probability space, under the hypotheses that the sequence of…

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…

We study the fluctuations of the eigenvalues of real valued large centrosymmetric random matrices via its linear eigenvalue statistic. This is essentially a central limit theorem (CLT) for sums of dependent random variables. The dependence…

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology…

In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

We prove a variant of the central limit theorem (CLT) for a sequence of i.i.d. random variables $\xi_j$, perturbed by a stochastic sequence of linear transformations $A_j$, representing the model uncertainty. The limit, corresponding to a…

The paper contains an exposition of recent as well as old enough results on determinantal random point fields. We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of the…

We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…

We derive a Central Limit Theorem (CLT) for $\log \left\vert\det \left( W_{N}-E_{N}\right)\right\vert,$ where $W_{N}$ is a Wigner matrix, and $E_{N}$ is local to the edge of the semi-circle law. Precisely, $E_N=2+N^{-2/3}\sigma_N$ with…

Let $X=\{X_n: n\in\mathbb{N}\}$ be the linear process defined by $X_n=\sum^{\infty}_{j=1} a_j\varepsilon_{n-j}$, where the coefficients $a_j=j^{-\beta}\ell(j)$ are constants with $\beta>0$ and $\ell$ a slowly varying function, and the…

Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the nonparametric local polynomial threshold estimator, especially local linear case, is employed to estimate the…