Related papers: Approximation of the integrated density of states …
We survey some aspects of the theory of the integrated density of states (IDS) of random Schroedinger operators. The first part motivates the problem and introduces the relevant models as well as quantities of interest. The proof of the…
We study finitely cyclic self-adjoint operators in a Hilbert space, i.e. self-adjoint operators that posses such a finite subset in the domain that the orbits of all its elements with respect to the operator are linearly dense in the space.…
In this work we obtain the integrated density of states for the Schr\"{o}dinger operators with decaying random potentials acting on $\ell^2(\mathbb{Z}^d)$. We also study the asymptotic of the largest and smallest eigenvalues of its finite…
The integrated density of states (IDS) is a fundamental spectral quantity for quantum Hamiltonians modeling condensed matter systems, describing how densely energy levels are distributed. It can be interpreted as a volume-averaged spectral…
We study the ergodic properties of Delone-Anderson operators, using the framework of randomly coloured Delone sets and Delone dynamical systems. In particular, we show the existence of the integrated density of states and, under some…
We investigate some bounds for the density of states in the pure point regime for the random Schr\"{o}dinger operators $H^{\omega}=-\Delta+\displaystyle\sum_{n\in\mathbb{Z}^d}a_nq_n(\omega)$, acting on $\ell^2(\mathbb{Z}^d)$, where…
We study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite…
We prove the algebraic eigenvalue conjecture of J. Dodziuk, P. Linnell, V. Mathai, T. Schick and S. Yates for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we define…
Reconstructing a density of states or similar distribution from moments or continued fractions is an important problem in calculating the electronic and vibrational structure of defective or non-crystalline solids. For single bands a…
We prove that the integrated density of surface states of continuous or discrete Anderson-type random Schroedinger operators is a measurable locally integrable function rather than a signed measure or a distribution. This generalize our…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
We consider the spectral properties of aperiodic block subwavelength resonator systems in one dimension, with a primary focus on the density of states. We prove that for random block configurations, as the number of blocks $M\to \infty$,…
For random operators it is conjectured that spectral properties of an infinite-volume operator are related to the distribution of spectral gaps of finite-volume approximations. In particular, localization and pure point spectrum in infinite…
We study discrete random Schr\"odinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green's function and…
We investigate how free probability allows us to approximate the density of states in tight binding models of disordered electronic systems. Extending our previous studies of the Anderson model in neighbor interactions [J. Chen et al.,…
We define a linear functional, the DOS functional, on spaces of holomorphic functions on the unit disk which is associated with random ergodic contraction operators on a Hilbert space, in analogy with the density of state functional for…
The approximation of a stationary time-series by finite order autoregressive (AR) and moving averages (MA) is a problem that occurs in many applications. In this paper we study asymptotic behavior of the spectral density of finite order…
We study infinite sums \[ {\mathcal P}_{\varkappa}=\sum_{n=-\infty}^\infty \varkappa_n \langle\cdot, \psi_n\rangle\psi_n \] of rank-one projections in a Hilbert space, where $\{\psi_n\}_{n\in\mathbb Z}$ are norm-one vectors, not necessarily…
We establish the absolute continuity of the integrated density of states (IDS) for quasi-periodic Schr\"odinger operators with a large trigonometric potential and Diophantine frequency. This partially solves Eliasson's open problem in 2002.…
We study spectra of Schr\"odinger operators on $\RR^d$. First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values…