Related papers: Moderate deviations for the determinant of Wigner …

We consider a branching random walk on $\mathbb{R}$ with a stationary and ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let $Z_n$ be the counting measure of particles of generation $n$ and $\tilde Z_n(t)=\int…

In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic…

We study the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix size goes to infinity. In the case of the Gaussian ensembles (GOE and GUE) this problem was considered by A.Lytova…

Let $\{X, X_{n}; n \geq 1\}$ be a sequence of i.i.d. non-degenerate real-valued random variables with $\mathbb{E}X^{2} < \infty$. Let $S_{n} = \sum_{i=1}^{n} X_{i}$, $n \geq 1$. Let $g(\cdot): ~[0, \infty) \rightarrow [0, \infty)$ be a…

We consider the quadratic form of a general deterministic matrix on the eigenvectors of an $N\times N$ Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large $N$ limit. The proof is a combination of…

We show that for local alternatives to uniformity which are determined by a sequence of square integrable densities the moderate deviation (MD) theorem for the corresponding Neyman-Pearson statistic does not hold in the full range for all…

For ${1/2}<\alpha<1$, we propose the MDP analysis for family $$ S^\alpha_n=\frac{1}{n^\alpha}\sum_{i=1}^nH(X_{i-1}), n\ge 1, $$ where $(X_n)_{n\ge 0}$ be a homogeneous ergodic Markov chain, $X_n\in \mathbb{R}^d$, when the spectrum of…

This is an elementary review, aimed at non-specialists, of results that have been obtained for the limiting distribution of eigenvalues and for the operator norms of real symmetric random matrices via the method of moments. This method goes…

Let $(Z_n)_{n\geq0}$ be a supercritical Galton-Watson process. Consider the Lotka-Nagaev estimator for the offspring mean. In this paper, we establish self-normalized Cram\'{e}r type moderate deviations and Berry-Esseen's bounds for the…

This paper studies quantitative deviation bounds for statistical ensembles evolving under the one-parameter flow of a nearly integrable Hamiltonian system. Combining Nekhoroshev-type stability estimates with phase-mixing arguments, we…

In the present paper, fixed trace $\beta$-Hermite ensembles generalizing the fixed trace Gaussian Hermite ensemble are considered. For all $\beta$, we prove the Wigner semicircle law for these ensembles by using two different methods: one…

The model of heavy Wigner matrices generalizes the classical ensemble of Wigner matrices: the sub-diagonal entries are independent, identically distributed along to and out of the diagonal, and the moments its entries are of order 1/N,…

We compute some exact results for the gap-ratio of mixed Wigner surmises for up to four eigenvalues and $0\leq\beta\leq4$. The main results concern equal mixtures of the GOE, GUE, and GSE random matrix classes. These give rise to…

It is a result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n\times n$ Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process…

This paper is devoted to the Gaussian fluctuations and deviations of the traces of tridiagonal random matrix. Under quite general assumptions, we prove that the traces are approximately normal distributed. Multi-dimensional central limit…

In this paper, we present sufficient conditions and criteria to establish the large and moderate deviation principle of multivalued McKean-Vlasov stochastic differential equation by means of the weak convergence method.

We provide sparse estimates for gradients of solutions to divergence form elliptic partial differential equations in terms of the source data. We give a general result of Meyers (or Gehring) type, a result for linear equations with VMO…

Assume a finite set of complex random variables form a determinantal point process, we obtain a theorem on the limit of the empirical distribution of these random variables. The result is applied to %We study the limits of the empirical…

The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of large real and complex Hermitian matrices with independent, identically distributed entries are universal in a sense that they depend only on the…

We establish large deviation principles for the extremal eigenvalues of the Ginibre ensembles with good rate functions. In contrast to the typical estimates for the extremal eigenvalues, the large deviations for the real Ginibre ensemble…