Related papers: Impurity models and products of random matrices
We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…
Motivated by recently emerging problems in machine learning and statistics, we propose data models which relax the familiar i.i.d. assumption. In essence, we seek to understand what it means for data to come from a set of probability…
This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability,…
The diagrammatic theory is proposed for the strongly correlated impurity Anderson model. The strongly correlated impurity electrons are hybridized with free conduction electrons. For this system the new diagrammatic approach is formulated.…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…
This work initiates the systematic study of explicit distributions that are indistinguishable from a single exponential-size combinatorial object. In this we extend the work of Goldreich, Goldwasser and Nussboim (SICOMP 2010) that focused…
We comprehend the role of imperfections in materials consisting of interacting particles, arising from different origins on their universal features. Specifically, we report the static and dynamic responses in a cluster of Coulomb…
The impurities, introduced intentionally or accidentally into certain materials, can significantly modify their characteristics or reveal their intrinsic physical properties, and thus play an important role in solid-state physics. Different…
Financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features. Here, we show that a pairwise maximum entropy model (or auto-logistic model) is able to describe switches…
In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…
We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and…
We study a simple exactly solvable 2D model describing the interaction of a localized particle with an impurity. The localization potential $V(x)=-\alpha \delta (x)$ causes the particle to be trapped in the y-axis, and the `impurity' is…
We consider periodically driven potential impurities coupled to the surface states of a two-dimensional topological insulator. The problem is addressed by means of two models, out which the first model is an effective continuum Hamiltonian…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
The single channel Anderson impurity model is a standard model for the description of magnetic impurities in metallic systems. Usually, the bandwidth represents the largest energy scale of the problem. In this paper, we analyze the limit of…
In some quasi-one-dimensional weakly disordered media, impurities are large and rare rather than small and dense. For an Anderson model with a low density of strong impurities, a perturbation theory in the impurity density is developed for…
We propose a random matrix modeling for the parametric evolution of eigenstates. The model is inspired by a large class of quantized chaotic systems. Its unique feature is having parametric invariance while still possessing the…
We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation…