35 citations · 68 across the 13 of their papers we have counts for
18 papers
Fluctuations and localization length for random band GOE matrix
Michael Goldstein
We prove that GOE random band matrix localization length is , where is the width of the band and is an absolute constant. Our method consist…
On the Spectrum of Multi-Frequency Quasiperiodic Schrödinger Operators with Large Coupling
Michael Goldstein, Wilhelm Schlag, Mircea Voda
We study multi-frequency quasiperiodic Schrödinger operators on . We prove that for a large real analytic potential satisfying certain restrictions the spectrum consis…
On localization and the spectrum of multi-frequency quasi-periodic operators
Michael Goldstein, Wilhelm Schlag, Mircea Voda
We study multi-frequency quasi-periodic Schrödinger operators on in the regime of positive Lyapunov exponent and for general analytic potentials. Combining Bourgain's…
Cartan Covers and Doubling Bernstein Type Inequalities on Analytic Subsets of
Michael Goldstein, Wilhelm Schlag, Mircea Voda
We prove a version of the doubling Bernstein inequalities for the trace of an analytic function of two variables on an analytic subset of . The estimate applies to th…
Almost Periodicity in Time of Solutions of the KdV Equation
Ilia Binder, David Damanik, Michael Goldstein +1
We study the Cauchy problem for the KdV equation with almost periodic initial data . We consider initial data $V…
Homogeneity of the spectrum for quasi-periodic Schrödinger operators
Michael Goldstein, David Damanik, Wilhelm Schlag +1
We consider the one-dimensional discrete Schrödinger operator , with real-ana…
A Multi-Scale Analysis Scheme on Abelian Groups with an Application to Operators Dual to Hill's Equation
David Damanik, Michael Goldstein, Milivoje Lukic
We present an abstract multiscale analysis scheme for matrix functions , where is an Abelian group equipped with a dist…
The Isospectral Torus of Quasi-Periodic Schrödinger Operators via Periodic Approximations
David Damanik, Michael Goldstein, Milivoje Lukic
We study the quasi-periodic Schrödinger operator in the regime of "small" $V(x) = \sum_{m\in\mathbb{Z}^ν}c(m)\exp (2πi mω…
On the Sum of the Non-Negative Lyapunov Exponents for Some Cocycles Related to the Anderson Model
Ilia Binder, Michael Goldstein, Mircea Voda
We provide an explicit lower bound for the the sum of the non-negative Lyapunov exponents for some cocycles related to the Anderson model. In particular, for the Anderson model on…
The Spectrum of a Schrödinger Operator With Small Quasi-Periodic Potential is Homogeneous
David Damanik, Michael Goldstein, Milivoje Lukic
We consider the quasi-periodic Schrödinger operator in , where the potential is given by $$ V(x) = \sum_{m \in \mathbb{Z}^ν\set…
On fluctuations and localization length for the Anderson model on a strip
Ilia Binder, Michael Goldstein, Mircea Voda
We consider the Anderson model on a strip. Assuming that potentials have bounded density with considerable tails we get a lower bound for the fluctuations of the logarithm of the G…
On the Existence and Uniqueness of Global Solutions for the KdV Equation with Quasi-Periodic Initial Data
David Damanik, Michael Goldstein
We consider the KdV equation with quasi-periodic initial data whose Fourier coefficients decay exponentially and prove existence…
On the Inverse Spectral Problem for the Quasi-Periodic Schrödinger Equation
David Damanik, Michael Goldstein
We study the quasi-periodic Schrödinger equation $$ -ψ"(x) + V(x) ψ(x) = E ψ(x), \qquad x \in \IR $$ in the regime of "small" . Let , $m \in \zv$, be the standard l…
On non-perturbative Anderson localization for C^αpotentials generated by shifts and skew-shifts
Jackson Chan, Michael Goldstein, Wilhelm Schlag
In this paper we address the question of proving Anderson localization (AL) for the operator [H(x,ω)ψ](n) := - \vp(n+1) - \vp(n-1) + V\bigl(T^n_ωx\bigr)ψ(n), n\in\mathbb Z where T:…
On resonances and the formation of gaps in the spectrum of quasi-periodic Schroedinger equations
Michael Goldstein, Wilhelm Schlag
We consider one-dimensional difference Schroedinger equations on the discrete line with a potential generated by evaluating a real-analytic potential function V(x) on the one-dimen…
On Schroedinger operators with dynamically defined potentials
Michael Goldstein, Wilhelm Schlag
We review some of the work by the authors on this topic. In particular, we discuss the recent paper "Fine properties of the IDS and a quantitative separation property of the Dirich…
Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues
Michael Goldstein, Wilhelm Schlag
We develop some non-perturbative methods for studying the IDS in almost Mathieu and related models. Assuming positive Lyapunov exponents, and assuming that the potential function i…
On nonperturbative localization with quasi-periodic potential
Jean Bourgain, Michael Goldstein
The two main results of the article are concerned with Anderson Localization for one-dimensional lattice Schroedinger operators with quasi-periodic potentials with d frequencies. F…