Related papers: Spectral and Dynamical Properties of Certain Rando…
Using the spectral theory of unitary operators and the theory of orthogonal polynomials on the unit circle, we propose a simple matrix model for the following circular analogue of the Jacobi ensemble: $$c_{\delta,\beta}^{(n)} \prod_{1\leq…
Using the Coulomb gas method and standard methods of statistical physics, we compute analytically the joint cumulative probability distribution of the extreme eigenvalues of the Jacobi-MANOVA ensemble of random matrices, in the limit of…
We derive a sequence of measures whose corresponding Jacobi matrices have special properties and a general mapping of an open quantum system onto 1D semi infinite chains with only nearest neighbour interactions. Then we proceed to use the…
We study the spectral properties of matrices of long-range percolation model. These are N\times N random real symmetric matrices H=\{H(i,j)\}_{i,j} whose elements are independent random variables taking zero value with probability…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
We consider continuum random Schr\"odinger operators of the type $H_{\omega} = -\Delta + V_0 + V_{\omega}$ with a deterministic background potential $V_0$. We establish criteria for the absence of continuous and absolutely continuous…
The circular and Jacobi ensembles of random matrices have their eigenvalue support on the unit circle of the complex plane and the interval $(0,1)$ of the real line respectively. The averaged value of the modulus of the corresponding…
The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows…
The Jacobi ensemble is one of the classical ensembles of random matrix theory. Prominent in applications are properties of the eigenvalues at the spectrum edge, specifically the distribution of the largest (e.g. Roy's largest root test in…
We form the Jacobi theta distribution through discrete integration of exponential random variables over an infinite inverse square law surface. It is continuous, supported on the positive reals, has a single positive parameter, is unimodal,…
The Wigner-von Neumann method, which was previously used for perturbing continuous Schr\"{o}dinger operators, is here applied to their discrete counterparts. In particular, we consider perturbations of arbitrary $T$-periodic Jacobi…
We consider discrete one-dimensional Schr\"odinger operators with quasi-Sturmian potentials. We present a new approach to the trace map dynamical system which is independent of the initial conditions and establish a characterization of the…
In this paper we approximate a Schr\"odinger operator on $L^2(\R)$ by Jacobi operators on $\ell^2(\Z)$ to provide new proofs of sharp Lieb-Thirring inequalities for the powers $\gamma=1/2$ and $\gamma=3/2$. To this end we first investigate…
This is an ultimate completion of our earlier paper [Acta.\ Math.\ Hungar.\ 140 (2013), 248--292] where mapping properties of several fundamental harmonic analysis operators in the setting of symmetrized Jacobi trigonometric expansions were…
In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schr\"odinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an…
We extend in this work the Jitomirskaya-Last inequality and Last-Simoncriterion for the absolutely continuous spectral component of a half-line Schr\"odinger operator to the special class of matrix-valued Jacobi operators…
We consider $C=A+B$ where $A$ is selfadjoint with a gap $(a,b)$ in its spectrum and $B$ is (relatively) compact. We prove a general result allowing $B$ of indefinite sign and apply it to obtain a $(\delta V)^{d/2}$ bound for perturbations…
We present results on the broadband nature of the power spectrum $S(\omega)$, $\omega\in(0,2\pi)$, for a large class of nonuniformly expanding maps with summable and nonsummable decay of correlations. In particular, we consider a class of…
Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$ \lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B, $$ with…
Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…