Preprints

2022

Positivity of the Lyapunov exponent for analytic quasiperiodic operators with arbitrary finitevalued background
, M. Powell

Continuity of the Lyapunov exponent for analytic multifrequency quasiperiodic cocycles
, M. Powell

Magnetic response of twisted bilayer graphene
, S. Becker, J. Kim, X. Zhu

Antiresonances and sharp analysis of Maryland localization for all parameters
, R. Han, S. Jitomirskaya, and F. Yang

Stability of the noncritical spectral properties I: arithmetic absolute continuity of the integrated density of states
, L. Ge, S. Jitomirskaya, and X. Zhao

2021

Must the spectrum of a Random Schrödinger operator contain an interval?
, D. Damanik, A. Gorodetski

A remark on inverse problems for nonlinear magnetic Schrödinger equations on complex manifolds
, K. Krupchyk, G. Uhlmann and L. Yan

Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schroedinger operators with smooth potentials
, S. Jitomirskaya and M. Powell

Localization for random CMV matrices
, X. Zhu

Reconstructing a potential perturbation of the biharmonic operator on transversally anisotropic manifolds
, L. Yan

Phase transition on phase: the interface
, S. Jitomirskaya and F. Yang

Antiresonances and sharp analysis of Maryland localization for all parameters
, R. Han, S. Jitomirskaya, and F. Yang

Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators with smooth potentials
, S. Jitomirskaya and M. Powell

Fine dimensional properties of spectral measures
, M. Landrigan and M. Powell

Upper bounds on transport exponents for long range operators
, S. Jitomirskaya and W. Liu

Transition space for the continuity of the Lyapunov exponent of quasiperiodic Schrödinger cocycles
, L. Ge, Y. Wang, J. You, X. Zhao

Global rigidity for ultradifferentiable quasiperiodic cocycles and its spectral applications
, H. Cheng, L. Ge, J. You, Q. Zhou

2020

Multidimensional Schrödinger Operators Whose Spectrum Features a HalfLine and a Cantor Set
, D. Damanik, J. Fillman, A. Gorodetski

Inverse boundary problems for biharmonic operators in transversally anisotropic geometries
, L. Yan

Logarithmic capacity of random G_{ δ}sets
, F. Quintino

On the spectra of separable 2D almost Mathieu operators
, A. Takase

Entanglement Entropy Bounds in the Higher Spin XXZ Chain
, C. Fischbacher and O. Ogunkoya

Growth of the WangCasatiProsen Counter in an Integrable Billiard
, Z. Hwang, C. Marx, J. Seaward, S. Jitomirskaya, and M. Olshanii

Hölder Regularity of the Integrated Density of States for QuasiPeriodic LongRange Operators on ℓ^{2}(Z^{d})
, L. Ge, J. You and X. Zhao

Ballistic Transport for OneDimensional QuasiPeriodic Schrödinger Operators
, L. Ge and I. Kachkovskiy

Honeycomb structures in magnetic fields
, S. Becker, R. Han, S. Jitomirskaya, M. Zworski

On the spectrum of critical Mathieu operators in the rational case
, S. Jitomirskaya, L. Konstantoniv, I. Krasovsky

Lower Bound to the Entanglement Entropy of the XXZ Spin Ring
, C. Fischbacher and R. Schulte

Holder Continuity of Absolutely Continuous Spectral Measure for the extended Harper's model
, X. Zhao

Arithmetic Version of Anderson Localization via Reducibility
, L. Ge and J. You

2019

Critical phenomena, arithmetic phase transitions, and universality: some recent results on the almost Mathieu operator. Lecture notes for CDM 2019.
, S. Jitomirskaya

Jean Bourgain (for the Remembrances article in Notices AMS)
, S. Jitomirskaya

Phase transition of capacity for the uniform Gdelta sets
, V. Kleptsyn, F. Quintino

Exponential Dynamical Localization for Random Word Models
, N. Rangamani

Alexander Gordon
, S. Jitomirskaya, S. A. Molchanov, B. Simon, B. R. Vainberg

On point spectrum of critical almost Mathieu
operators
, S. Jitomirskaya

Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case
, S. Jitomirskaya, W. Liu

Anderson localization for multifrequency quasiperiodic operators on Zd
, S. Jitomirskaya, W. Liu

Spectral theory of SchroÌˆdinger operators over circle diffeomorphisms, S. Jitomirskaya, S. Kocic

Critical almost Mathieu operator: hidden singularity, gap continuity, and the Hausdorff dimension of the spectrum, S. Jitomirskaya, I. Krasovsky

Arithmetic spectral transitions: a competition between hyperbolicity and the arithmetics of small denominators, S. Jitomirskaya, W. Liu, and S. Zhang

2018

Large deviations of the Lyapunov exponent and localization for the 1D Anderson model, S. Jitomirskaya, X. Zhu

UnboundedSingular Random Jacobi Matrices, N. Rangamani

Fractal dimension of spectral measures of rank one perturbations of probability measures, M. Powell

S. Jitomirskaya, W. Liu,
Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the
essential spectrum of the Laplacian.
arXiv version

W. Liu, D. Ong,
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Schrödinger operators.
arXiv version

W. Liu, D. Ong,
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators.
arXiv version

W. Liu, Criteria for embedded eigenvalues for discrete Schrödinger operators.
arXiv version

W. Liu, Almost Mathieu operators with completely resonant phases.
arXiv version

W. Liu, Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators.
arXiv version

W. Liu, The asymptotical behaviour of the embedded eigenvalue for perturbed periodic operators.
arXiv version

W. Liu, Absence of singular continuous spectrum for perturbed discrete Schrödinger operators.
arXiv version

S. Jitomirskaya, W. Liu, and S. Zhang,
Arithmetic spectral transitions. To appear to AMS/PCMI, Harmonic Analysis, 2018 .

Multidimensional AlmostPeriodic Schrodinger Operators with Cantor Spectrum,
D. Damanik, J. Fillman, A. Gorodetski

Parametric Furstenberg Theorem on Random Products of SL(2,R) matrices,
A. Gorodetski, V. Kleptsyn

Large deviations of the Lyapunov exponent and localization for the 1D Anderson model,
S. Jitomirskaya and X. Zhu

Cantor spectrum of graphene in magnetic fields,
S. Becker, R. Han, and S. Jitomirskaya

Inhomogeneous Diophantine approximation in the coprime setting,
S. Jitomirskaya and W. Liu

Universal reflectivehierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase,
S. Jitomirskaya and W. Liu

2017

Spectral transition line for the extended Harper's model in the positive Lyapunov exponent regime,
F. Yang

Discrete BetheSommerfeld Conjecture,
R. Han and S. Jitomirskaya

Growth of the eigensolutions of Laplacians on Riemmannian manifolds I: construction of energy function,
W. Liu

Growth of the eigensolutions of Laplacians on Riemmannian manifolds II: positivity of the initial energy,
W. Liu

Some refined results on mixed Littlewood conjecture for pseudoabsolute values,
W. Liu

Sharp bound on the largest positive eigenvalue for onedimensional Schrodinger operators,
W. Liu

Upper bounds on the spectral gaps of the quasiperiodic Schrodinger operators with Liouville frequencies,
W. Liu and Y. Shi [submitted]

Large coupling asymptotics of the Lyapunov exponent for quasiperiodic Schrodinger operators with analytic potentials,
R. Han, C. Marx

2016

Continuity of measure of the spectrum of Schrodinger operators with potentials defined by shifts and skewshifts on higher dimensional tori,
R. Han

Sch'nol's theorem and the spectrum of long range operators,
R. Han

Generic continuous spectrum for multidimensional quasi periodic Schrodinger operators with rough potentials,
Y. Fan, R. Han

Full measure reducibility and localization for quasiperiodic Jacobi operators: a topological criterion,
R. Han, S. Jitomirskaya

Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy,
R. Han, S. Jitomirskaya

The Mobius transformation of continued fractions with bounded upper and lower partial quotients,
W. Liu

A short proof of the HRT conjecture for almost every (1,3) configuration,
W. Liu

A lower bound on the Lyapunov exponent for the generalized Harper's model,
S. Jitomirskaya, W. Liu

Universal hierarchical structure of quasiperiodic eigenfunctions,
S. Jitomirskaya, W. Liu

The spectra of surface Maryland model for all phases,
W. Liu

Singular continuous spectrum for singular potential,
S. Jitomirskaya, F. Yang

Dry Ten Martini problem for the nonselfdual extended Harper's model,
R. Han

Quantum and spectral properties of the Labyrinth model,
Y. Takahashi

Products of two Cantor sets,
Y. Takahashi

Sums of regular Cantor sets of large dimension and the square Fibonacci Hamiltonian,
D. Damanik, A. Gorodetski

2015

An Extension of the KunzSouillard Approach to Localization in One Dimension and Applications to AlmostPeriodic Schrodinger Operators,
D. Damanik, A. Gorodetski

On the sums of nearly affine Cantor sets,
A. Gorodetski, S. Northrup

Path connectedness and entropy density of the space of hyperbolic ergodic measures,
A. Gorodetski, Y. Pesin

Transport exponents of Sturmian Hamiltonians,
D. Damanik, A. Gorodetski, QingHui Liu, YanHui Qu

Asymptotics of quasiperiodic eigenfunctions,
S. Jitomirskaya, W. Liu

Arithmetic spectral transitions for the Maryland model,
S. Jitomirskaya, W. Liu

Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrodinger operators,
S. Jitomirskaya, S. Zhang

Mixed spectral types for the one frequency discrete quasiperiodic Schrodinger operator,
S. Zhang

On the structure of band edges of 2d periodic elliptic operators,
N. Filonov, I. Kachkovskiy

All couplings localization for quasiperiodic operators with Lipschitz monotone potentials,
S. Jitomirskaya, I. Kachkovskiy

On transport properties of isotropic quasiperiodic XY spin chains,
I. Kachkovskiy

$L^2$reducibility and localization for quasiperiodic operators
,
S. Jitomirskaya, I. Kachkovskiy

Mixed spectral regimes for square Fibonacci Hamiltonians,
J. Fillman, Y. Takahashi, W. Yessen

Dynamics and spectral theory of quasiperiodic Schrodingertype operators ,
S. Jitomirskaya, C. Marx

Uniform localization is always uniform,
R. Han

2014

Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians,
D. Damanik, A. Gorodetski

Synchronization properties of random piecewise isometries,
A. Gorodetski, V. Kleptsyn

The Fibonacci Hamiltonian,
D. Damanik, A. Gorodetski, W. Yessen

Dynamical bounds for quasiperiodic Schrodinger operators with rough potentials,
S. Jitomirskaya, R. Mavi

Almost Commuting Elements in
NonCommutative Symmetric Operator Spaces. PhD Thesis.
,
M. Said

On the distance
to normal elements in $C^*$algebras of real rank zero,
I. Kachkovskiy, Y. Safarov

2013

Spectra of Discrete Schrodinger Operators with Primitive Invertible Substitution Potentials, M. Mei

Spectral Theory for Extended Harper's Model, S.Jitomirskaya, C. Marx

POINT SPECTRUM FOR QUASIPERIODIC LONG RANGE OPERATORS, J. You, S. Zhang, and Q. Zhou

Complex onefrequency cocycles, A.Avila, S.Jitomirskaya, C.Sadel

On the ground state calculation of a manybody system using a
selfconsistent basis and quasiMonte Carlo. An application to water
hexamer., I.Georgescu, S.Jitomirskaya, and V. Mandelshtam

Bootstrap multiscale analysis and localization for multiparticle continuous Anderson Hamiltonians, A.Klein, S.Nguyen

Ground state energy of trimmed discrete SchrÃƒÂ¶dinger operators and localization for trimmed Anderson models, A. Elgart,A.Klein

Translation numbers define generators of $F_k^+\to {\text{\rm Homeo}_+}(\mathbb{S}^1)$, T.GolenishchevaKutuzova, A.Gorodetski, V.Kleptsyn, and D.Volk

Absolutely Continuous Convolutions of Singular Measures and an Application to the Square Fibonacci Hamiltonian, D. Damanik, A. Gorodetski,
and B.Solomyak 
Spectral Properties of Schrodinger Operators Arising in the Study of Quasicrystals, D. Damanik, M. Embree, and A. Gorodetski 
Continuum Schrodinger Operators Associated With Aperiodic Subshifts, D. Damanik, A. Gorodetski,
and J.Fillman 
Almost Ballistic Transport for the Weakly Coupled Fibonacci Hamiltonian, D. Damanik and A. Gorodetski

2012

The Williams Bjerknes Model on Regular Trees, O. Louidor, R. Tessler, A. VandenbergRodes

Trapping in the random conductance model, A. VandenbergRodes (with Marek Biskup, Oren Louidor, and Alex Rozanov)

Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian, D. Damanik and A. Gorodetski

Continuity of the measure of the spectrum for quasiperiodic Schrödinger operators with rough potentials, S. Jitomirskaya and R. Mavi

Local estimates of exponential polynomials and their applications to inequalities of uncertainty principle type  part I, C. Marx

Exponential dynamical localization for the almostMathieu operator, H. Krüger and S. Jitomirskaya

Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients, I. The essential support of the measure, D. Damanik, P. Munger and W. Yessen

Absolutely continuous spectrum for random Schrödinger
operators on the Bethe strip , A. Klein and C. Sadel

Relations between transfer and scattering matrices in the presence of hyperbolic channels ,
C. Sadel

Analytic quasiperodic cocycles with singularities and the Lyapunov Exponent of Extended Harper's Model,
S. Jitomirskaya and C. Marx

Analytic quasiperiodic SchrÃ¶dinger operators and rational frequency approximants,
S. Jitomirskaya and C. Marx

Properties of 1D classical and quantum Ising quasicrystals: rigorous results, W. Yessen

The bootstrap multiscale analysis for the multiparticle Anderson model
, A. Klein, S.Nguyen

The AizenmanSimsStarr scheme and Parisi formula for mixed pspin spherical models, W. Chen

An approach to chaos in some mixed pspin models, W. Chen (with D. Panchenko)

2011

Spectral analysis of tridiagonal Fibonacci Hamiltonians, W. Yessen

On the spectrum of 1D quantum Ising quasicrystal, W. Yessen

The density of states measure for the weakly coupled Fibonacci Hamiltonian, D. Damanik and A. Gorodetski

On stochastic sea of the standard map, A. Gorodetski

Local
Wegner and Minami estimates for continuos random
Schrödinger operators , JM. Combes, F. Germinet, and
A. Klein

Bounds on the density of states for Schrödinger operators
, J. Bourgain and Abel Klein

A
comprehensive proof of localization for continuous Anderson
models with singular random potentials , F. Germinet,
A. Klein

Typical localization in the disordered continuum percolation model ,
R. Mavi

Relations between transfer and scattering matrices in the presence of hyperbolic channels ,
C. Sadel

Disorder Chaos in the SherringtonKirkpatrick Model with External Field, W. Chen

On the Mixed EvenSpin SherringtonKirkpatrick Model with Ferromagnetic Interaction, W. Chen

Reports, Conference Proceedings, Expository Notes, etc.

Spectral Properties of Quasicrystals via Analysis, Dynamics, and Geometric Measure Theory,
(includes contribution by D. Damanik, A. Gorodetski, V. Kleptsyn, R. Han, I. Kachkovskiy, Y. Takahashi, S. Zhang)

Oberwolfach report of Arbeitsgemeinschaft on Quasiperiodic Schrödinger Operators (Apr. 1  7, 2012),
(includes contribution by R. Mavi, C. Marx, Y. Wang and W. Yessen)

Oberwolfach report of MiniWorkshop on Dynamics of Trace Maps and Applications to Spectral Theory (Jan. 16  22, 2011),
(includes contribution by A. Gorodetski and W. Yessen)
