Related papers: Local eigenvalue statistics for higher-rank Anders…
The problem of simultaneous estimation of location/scale parameters $\theta_1$ and $\theta_2$ of a general bivariate location/scale model, when the ordering between the parameters is known apriori (say, $\theta_1\leq \theta_2$), has been…
In this paper we revisit a two-level discretization based on the Localized Orthogonal Decomposition (LOD). It was originally proposed in [P.Henning, A.M{\aa}lqvist, D.Peterseim. SIAM J. Numer. Anal.52-4:1525-1550, 2014] to compute ground…
We study, at zero temperature, the dynamics of a single electron in a Holstein model augmented by site-diagonal, binary-alloy type disorder. The average over the phonon vacuum and the alloy configurations is performed within a generalized…
We show analytically that the apparent non-analyticity discovered recently in the inverse participation ratio (IPR) of the eigenstates in Anderson's model of localization is also present in a simple two-site model, along with a concurrent…
We consider the distribution function $P(|\psi|^{2})$ of the eigenfunction amplitude at the center-of-band (E=0) anomaly in the one-dimensional tight-binding chain with weak uncorrelated on-site disorder (the one-dimensional Anderson…
We present a detection problem where several spatially distributed sensors observe Poisson signals emitted from a single source of unknown position. The measurements at each sensor are modeled by independent inhomogeneous Poisson processes.…
We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
In this paper, quantitative bounds in high-frequency central limit theorems are derived for Poisson based $U$-statistics of arbitrary degree built by means of wavelet coefficients over compact Riemannian manifolds. The wavelets considered…
Consider a bound state (an eigenfunction) $\psi$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $\gamma$ and of the one-particle kinetic energy density matrix $\tau$ associated with $\psi$. The paper…
The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional…
The one-dimensional (1d) Anderson model (AM) has statistical anomalies at any rational point $f=2a/\lambda_{E}$, where $a$ is the lattice constant and $\lambda_{E}$ is the de Broglie wavelength. We develop a regular approach to anomalous…
We consider the local statistics of $H = V^* X V + U^* Y U$ where $V$ and $U$ are independent Haar-distributed unitary matrices, and $X$ and $Y$ are deterministic real diagonal matrices. In the bulk, we prove that the gap statistics and…
We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are…
We study the Anderson transition for three-dimensional (3D) $N \times N \times N$ tightly bound cubic lattices where both real and imaginary parts of onsite energies are independent random variables distributed uniformly between $-W/2$ and…
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' $q$-nonextensive statistics.…
Localization to delocalization transitions in eigenfunctions are studied for finite interacting boson systems by employing one- plus two-body embedded Gaussian orthogonal ensemble of random matrices [EGOE(1+2)]. In the first analysis,…
We introduce a system of two linearly coupled discrete nonlinear Schr\"{o}dinger equations (DNLSEs), with the coupling constant subject to a rapid temporal modulation. The model can be realized in bimodal Bose-Einstein condensates (BEC).…
Combining the self-consistent theory of localization and the dynamical mean-field theory, we present a theoretical approach capable of describing both self-trapping of charge carriers during the process of polaron formation and…
We present numerical results for the statistics of $z$'s ($z$'s are defined as logarithm of eigenvalues of the transfermatrix $T^\dag T$) at the critical points of Anderson transition in 3D and 4D. The change of the density of $z$ due to…