Related papers: Localization for heavy-tailed Anderson models
We study a lattice sigma model which is expected to reflect the Anderson localization and delocalization transition for real symmetric band matrices in 3D. In this statistical mechanics model, the field takes values in a supermanifold based…
We establish non-perturbative Anderson localization for a wide class of 1D quasiperiodic operators with unbounded monotone potentials, extending the classical results on Maryland model and perturbative results for analytic potentials by…
Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…
Localization of electronic states in disordered thin layered systems with b layers is studied within the Anderson model of localization using the transfer-matrix method and finite-size scaling of the inverse of the smallest Lyapunov…
We compute the distribution function of single-level curvatures, $P(k)$, for a tight binding model with site disorder, on a cubic lattice. In metals $P(k)$ is very close to the predictions of the random-matrix theory (RMT). In insulators…
We examine the onset of Anderson localization in three-dimensional systems with structural disorder in the form of lattice irregularities and in the absence of any on-site disordered potential. Analyzing two models with distinct types of…
The localization behavior of the Anderson model with anisotropic hopping integral t for weakly coupled planes and weakly coupled chains is investigated both numerically with the transfer matrix method and analytically within the…
This paper proposes a new test for a change point in the mean of high-dimensional data based on the spatial sign and self-normalization. The test is easy to implement with no tuning parameters, robust to heavy-tailedness and theoretically…
We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in…
We study the problem of factor modelling vector- and tensor-valued time series in the presence of heavy tails in the data, which produce extreme observations with non-negligible probability. We propose to combine a two-step procedure for…
We study spatial structures of anomalously localized states (ALS) in tail regions at the critical point of the Anderson transition in the two-dimensional symplectic class. In order to examine tail structures of ALS, we apply the…
We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\ the right tail of its large deviations). The results also transfer to the left tail…
We study high-dimensional signal recovery from non-linear measurements with design vectors having elliptically symmetric distribution. Special attention is devoted to the situation when the unknown signal belongs to a set of low statistical…
In this note we show that in any dimension $d$, the strong disorder property implies the strong localization property. This is established for a continuous time model of directed polymers in a random environment : the parabolic Anderson…
We provide a statistical characterization of the ionization yield of one-dimensional, periodically driven Rydberg states of atomic hydrogen, in the spirit of Anderson localization theory. We find excellent agreement with predictions for the…
Nonreciprocity breaks the symmetry between forward and backward propagation, giving rise to a range of peculiar wave phenomena. In this work, we investigate Anderson localization in higher-dimensional nonreciprocal lattices. Focusing on the…
We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the L\'evy matrices proposed by Bouchaud and Cizeau, as well as sparse random matrices with O(1) non-zero entries…
We obtain for the first time the expressions for the mean and the variance of the transmission coefficient for an Anderson chain in the weak localization regime, using exact expansions of the complex transmission- and reflection…
We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud…
The entanglement in one-dimensional Anderson model is studied. We show that the pairwise entanglement measured by the average concurrence has a direct relation to the localization length. The numerical study indicates that the disorder…