Related papers: Level Repulsion for a class of decaying random pot…
A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity.…
Contrary to the theoretical predictions that all waves in two-dimensional disordered materials are localized, Anderson localization is observed only for sufficiently high frequencies in an isotropically jammed two-dimensional disordered…
We consider discrete one-dimensional random Schroedinger operators with decaying matrix-valued, independent potentials. We show that if the l^2-norm of this potential has finite expectation value with respect to the product measure then…
We establish a quantitative criterion for an operator defined on a Galton-Watson random tree for having an absolutely continuous spectrum. For the adjacency operator, this criterion requires that the offspring distribution has a relative…
We study the level statistics of one-dimensional Schr\"odinger operator with random potential decaying like $x^{-\alpha}$ at infinity. We consider the point process $\xi_L$ consisting of the rescaled eigenvalues and show that : (i)(ac…
We investigate the scaling properties of the two-dimensional (2D) Anderson model of localization with purely off-diagonal disorder (random hopping). In particular, we show that for small energies the infinite-size localization lengths as…
We study the critical behaviour of Anderson localized modes near intersecting flat and dispersive bands in the quasi-one-dimensional diamond ladder with weak diagonal disorder $W$. The localization length $\xi$ of the flat band states…
We calculate numerically the entanglement entropy of free fermion ground states in one-, two- and three-dimensional Anderson models, and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than…
We consider random graphs with uniformly bounded edges on a Poisson point process conditioned to contain the origin. In particular we focus on the random connection model, the Boolean model and Miller-Abrahams random resistor network with…
We study the rate of correlation decay in the two-dimensional random-field Ising model at weak field strength $\varepsilon$. We combine elements of the recent proof of exponential decay of correlations with a quantitative refinement of a…
We study the surface scaling behavior of a semi-infinite $d$-dimensional O(N) spin system in the presence of quenched random field and random anisotropy disorders. It is known that above the lower critical dimension $d_{\mathrm{lc}}=4$ the…
We consider the Constrained-degree percolation model in random environment (CDPRE) on the square lattice. In this model, each vertex $v$ has an independent random constraint $\kappa_v$ which takes the value $j\in \{0,1,2,3\}$ with…
We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting…
The energy level statistics of 2D electrons with spin-orbit scattering are considered near the disorder induced metal-insulator transition. Using the Ando model, the nearest-level-spacing distribution is calculated numerically at the…
We study spectral properties of partial differential operators modelling composite materials with highly contrasting constituents, comprised of soft spherical inclusions with random radii dispersed in a stiff matrix. Such operators have…
This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is wide enough to include popular high breakdown point estimators such as…
The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice $\mathbb{Z}^d$, $d\ge1$, because it fulfills several stylized facts observed in large…
We prove that the eigenvalues of a continuum random Schr\"odinger operator $-\Delta+ V_{\omega}$ of Anderson type, with complex decaying potential, can be bounded (with high probability) in terms of an $L^q$ norm of the potential for all…
The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for…
The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent $\nu$ of the localization length is extracted and estimated to be $\nu = 1.3 \pm 0.2$.…