相关论文: Exponential growth of random determinants beyond i…

We investigate the eigenvalues statistics of ensembles of normal random matrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We…

We construct explicit deterministic extractors for polynomial images of varieties, that is, distributions sampled by applying a low-degree polynomial map $f : \mathbb{F}_q^r \to \mathbb{F}_q^n$ to an element sampled uniformly at random from…

This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of…

We continue the development of the study of the equisingularity of isolated singularities, in the determinantal case. This version of the paper includes a substantial amount of new material (76% larger). The new material introduces the idea…

Given a square, nonsingular matrix of univariate polynomials $\mathbf{F}\in\mathbb{K}[x]^{n\times n}$ over a field $\mathbb{K}$, we give a deterministic algorithm for finding the determinant of $\mathbf{F}$. The complexity of the algorithm…

Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of…

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,…

In this article, we obtain a super-exponential rate of convergence in total variation between the traces of the first $m$ powers of an $n\times n$ random unitary matrices and a $2m$-dimensional Gaussian random variable. This generalizes…

Complex eigenvalues of random matrices $J=\text{GUE }+ i\gamma \diag (1, 0, \ldots, 0)$ provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the…

We consider the ensemble of adjacency matrices of Erd{\H o}s-R\'enyi random graphs, i.e.\ graphs on $N$ vertices where every edge is chosen independently and with probability $p \equiv p(N)$. We rescale the matrix so that its bulk…

We define the empirical spectral distribution (ESD) of a random matrix polynomial with invertible leading coefficient, and we study it for complex $n \times n$ Gaussian monic matrix polynomials of degree $k$. We obtain exact formulae for…

We define a new diffusive matrix model converging towards the $\beta$ -Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…

We study the eigenvalues and the eigenvectors of $N\times N$ structured random matrices of the form $H = W\tilde{H}W+D$ with diagonal matrices $D$ and $W$ and $\tilde{H}$ from the Gaussian Unitary Ensemble. Using the supersymmetry technique…

We study higher order determinantal varieties obtained by considering generic $m\times n$ ($m \le n$) matrices over rings of the form $F[t]/(t^k)$, and for some fixed $r$, setting the coefficients of powers of $t$ of all $r \times r$ minors…

A novel scenario for the emergence of geometry in random multitrace matrix models of a single hermitian matrix $M$ with unitary $U(N) $ invariance, i.e. without a kinetic term, is presented. In particular, the dimension of the emergent…

We present large deviations principles for the moments of the empirical spectral measure of Wigner matrices and empirical measure of $\beta$-ensembles in three cases : the case of Wigner matrices without Gaussian tails, that is Wigner…

In this paper, we propose a simple inferential method for a wide class of panel data models with a focus on such cases that have both serial correlation and cross-sectional dependence. In order to establish an asymptotic theory to support…

A new characterization of the exponential distribution is established. It is proven that the well-known Sukhatme-Renyi necessary condition is also sufficient for exponentiality. A method of proof due to Arnold and Villasenor based on the…

In this article, we introduce a notion of an exponential matrix, which is a polynomial matrix with exponential properties, and a notion of an equivalence relation of two exponential matrices, and then we initiate to study classifying…

We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence…