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Related papers: Localization for heavy-tailed Anderson models

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This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the…

Disordered Systems and Neural Networks · Physics 2012-05-15 F. M. Izrailev , A. A. Krokhin , N. M. Makarov

The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…

Statistics Theory · Mathematics 2026-04-02 Axel Bücher , Yeonjoon Choi , Katharina Effertz , Stanislav Volgushev

We have been investigating the problem of the Anderson localization in a disordered one dimensional tight-binding model. The disorder is created by the interaction of mobile particles with other species, immobilized at random positions. We…

Quantum Gases · Physics 2016-11-23 Jan Major

We show, using quasi-exact numerical simulations, that Anderson localization of one-dimensional particles in a disordered potential survives in the presence of attractive interaction between particles. The localization length of the…

We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the $\mathbb{Z}^d$ lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical…

Mathematical Physics · Physics 2024-08-16 Nishant Rangamani , Xiaowen Zhu

We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…

Statistics Theory · Mathematics 2018-01-17 Stanislav Minsker , Xiaohan Wei

We introduce a family of trees that interpolate between the Bethe lattice and $\bbZ$. We prove complete localization for the Anderson model on any member of that family.

Spectral Theory · Mathematics 2009-11-11 Jonathan Breuer

We present numerical simulations of disordered stealthy hyperuniform layered media ranging up to 10,000 thin slabs of high-dielectric constant separated by intervals of low dielectric constant that show no apparent evidence of Anderson…

Disordered Systems and Neural Networks · Physics 2025-07-31 Michael A. Klatt , Paul J. Steinhardt , Salvatore Torquato

In a recent publication, J. Phys.: Condens. Matt. 14 13777 (2002), Kuzovkov et. al. announced an analytical solution of the two-dimensional Anderson localisation problem via the calculation of a generalised Lyapunov exponent using signal…

Disordered Systems and Neural Networks · Physics 2009-11-10 P. Markoš , L. Schweitzer , M. Weyrauch

We extend the bootstrap multiscale analysis developed by Germinet and Klein to the multi-particle continuous Anderson Hamiltonian, obtaining Anderson localization with finite multiplicity of eigenvalues, decay of eigenfunction correlations,…

Mathematical Physics · Physics 2014-04-16 Abel Klein , Son Nguyen

We characterize the soft modes of the dynamical matrix at the depinning transition, and compare it with the properties of the Anderson model (and long--range generalizations). The density of states at the edge of the spectrum displays a…

Disordered Systems and Neural Networks · Physics 2018-02-15 Xiangyu Cao , Sebastian Bouzat , Alejandro B. Kolton , Alberto Rosso

The dominant approaches to text representation in natural language rely on learning embeddings on massive corpora which have convenient properties such as compositionality and distance preservation. In this paper, we develop a novel method…

A common object to describe the extremal dependence of a $d$-variate random vector $X$ is the stable tail dependence function $L$. Various parametric models have emerged, with a popular subclass consisting of those stable tail dependence…

Statistics Theory · Mathematics 2026-01-21 Alexis Boulin , Axel Bücher

Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the…

Disordered Systems and Neural Networks · Physics 2015-03-19 Alexander Croy , Philipp Cain , Michael Schreiber

This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…

Statistics Theory · Mathematics 2023-05-24 Kangqiang Li , Yuxuan Wang

This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used…

Machine Learning · Computer Science 2016-04-19 Daniel Hsu , Sivan Sabato

In this paper, we use recent breakthroughs in the study of coupled subwavelength resonator systems to reveal new insight into the mechanisms responsible for the fundamental features of Anderson localization. The occurrence strong…

Disordered Systems and Neural Networks · Physics 2023-07-21 Habib Ammari , Bryn Davies , Erik Orvehed Hiltunen

We introduce and prove local Wegner estimates for continuous generalized Anderson Hamiltonians, where the single-site random variables are independent but not necessarily identically distributed. In particular, we get Wegner estimates with…

Mathematical Physics · Physics 2013-09-18 Jean-Michel Combes , François Germinet , Abel Klein

We examine the use of distributions in numerical treatments of Anderson localisation and supply evidence that treating exponential localisation on Bethe lattices recovers the overall picture known from hypercubic lattices in 3d.

Strongly Correlated Electrons · Physics 2007-05-23 A. Alvermann , G. Schubert , A. Weisse , F. X. Bronold , H. Fehske

We report on phenomenon of Anderson-type localization of walking solitons in optical lattices with random frequency modulation, manifested as dramatic enhancement of soliton trapping probability on lattice inhomogeneities with growth of the…

Optics · Physics 2009-11-11 Yaroslav V. Kartashov Victor A. Vysloukh