Related papers: Local semicircle law in the bulk for Gaussian $\be…
We prove that the largest eigenvalues of the beta ensembles of random matrix theory converge in distribution to the low-lying eigenvalues of the random Schroedinger operator -d^2/dx^2 + x + (2/beta^{1/2}) b_x' restricted to the positive…
We develop a new method for deriving local laws for a large class of random matrices. It is applicable to many matrix models built from sums and products of deterministic or independent random matrices. In particular, it may be used to…
Beta Laguerre ensembles which are generalizations of Wishart ensembles and Laguerre ensembles can be realized as eigenvalues of certain random tridiagonal matrices. Analogous to the Wishart ($\beta=1$) case and the Laguerre ($\beta = 2$)…
We consider real, Gauss-divisible matrices $A_{t}=A+\sqrt{t}B$, where $B$ is from the real Ginibre ensemble. We prove that the bulk correlation functions converge to a universal limit for $t=O(N^{-1/3+\epsilon})$ if $A$ satisfies certain…
We study the Circular and Jacobi $\beta$-Ensembles and prove Gaussian fluctuations for the number of points in one or more intervals in the macroscopic scaling limit.
We study embedding a subset $K$ of the unit sphere to the Hamming cube $\{-1,+1\}^m$. We characterize the tradeoff between distortion and sample complexity $m$ in terms of the Gaussian width $\omega(K)$ of the set. For subspaces and several…
This paper studies the binary classification of two distributions with the same Gaussian copula in high dimensions. Under this semiparametric Gaussian copula setting, we derive an accurate semiparametric estimator of the log density ratio,…
We apply optimum experimental design (OED) to organic semiconductors modeled by the extended Gaussian disorder model (EGDM) which was developed by Pasveer et al. We present an extended Gummel method to decouple the corresponding system of…
We prove local boundedness for a quasilinear parabolic equation on the Heisenberg group \[ \partial_t u(\xi,t) + \text{p.v.}\int_{\mathbb{H}^N} \frac{|u(\xi,t)-u(\eta,t)|^{p-2}(u(\xi,t)-u(\eta,t))}{|\eta^{-1}\circ \xi|^{Q+sp}} \,d\eta = 0,…
We consider the symmetric tridiagonal matrix-valued process associated with Gaussian beta ensemble (G$\beta$E) by putting independent Brownian motions and Bessel processes on the diagonal entries and upper (lower)-diagonal ones,…
We study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie-Weiss-type. We provide a criterion on the correlations ensuring the validity of Wigner's semicircle law for the…
In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given by Dumitriu and Edelman. We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions…
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…
A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for…
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…
We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not…
Mesoscopic theory for self-assembling systems near a planar confining surface is developed. Euler- Lagrange (EL) equations and the boundary conditions (BC) for the local volume fraction and the correlation function are derived from the DFT…
We introduce a new technique for reducing the dimension of the ambient space of low-degree polynomials in the Gaussian space while preserving their relative correlation structure, analogous to the Johnson-Lindenstrauss lemma. As…
We determine the rate region of the Gaussian scalar-help-vector source-coding problem under a covariance matrix distortion constraint. The rate region is achieved by a Gaussian achievable scheme. We introduce a novel outer bounding…
Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is…