Related papers: Localization properties of the sparse Barrat-M\'ez…
This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The…
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…
We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening…
We study diffusion on a substrate with permanent traps distributed with critical positional correlation, modeled by their placement on the perimeters of a critical percolation cluster. We perform a numerical analysis of the vibrational…
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…
We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…
Sparse support recovery arises in many applications in communications and signal processing. Existing methods tackle sparse support recovery problems for a given measurement matrix, and cannot flexibly exploit the properties of sparsity…
This paper introduces an elasticity reconstruction method based on local displacement observations of elastic bodies. Sparse reconstruction theory is applied to formulate the underdetermined inverse problems of elasticity reconstruction…
We present a method to demonstrate Anderson localization in an optically induced randomized potential. By usage of computer controlled spatial light modulators, we are able to implement fully randomized nondiffracting beams of variable…
It is well-known that both branching random walk models and trap models can exhibit intermittency and localisation phenomena; the prototypical examples being the parabolic Anderson and Bouchaud trap models respectively. Our aim is to…
The properties of the entanglement entropy (EE) in one-dimensional disordered interacting systems are studied. Anderson localization leaves a clear signature on the average EE, as it saturates on length scale exceeding the localization…
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…
Phase retrieval can be expressed as one non-convex constrained optimization problem to identify one phase minimizer in the primal space. Many iterative transform techniques have been proposed to identify the minimizer, e.g., relaxed…
We study multi-particle interactive quantum disordered systems on a polynomially-growing countable connected graph (Z,E). The novelty is to give localization bounds uniform in finite or infinite volumes (subgraphs) in Z^N as well as for the…
Localization phenomena permeate many branches of physics playing a fundamental role on dynamical processes evolving on heterogeneous networks. These localization analyses are frequently grounded, for example, on eigenvectors of adjacency or…
Sparse autoencoders provide a promising unsupervised approach for extracting interpretable features from a language model by reconstructing activations from a sparse bottleneck layer. Since language models learn many concepts, autoencoders…
The localization phenomena due to the random potential scattering is widely discussed in the electron and photon systems, where the theoretical approach is the nonlinear $\sigma$ model with the replica method or with the supersymmetry. In…
In this work we study the spectral properties of the adjacency matrix of critical Erd\"os-R\'enyi (ER) graphs, i.e. when the average degree is of order \log N. In a series of recent inspiring papers Alt, Ducatez, and Knowles have rigorously…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
We introduce novel characterizations for many-body phase transitions between delocalized and localized phases based on the system's sensitivity to boundary conditions. In particular, we change boundary conditions from periodic to…