Preprints

2022
  • Positivity of the Lyapunov exponent for analytic quasiperiodic operators with arbitrary finite-valued background , M. Powell
  • Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles , M. Powell
  • Magnetic response of twisted bilayer graphene , S. Becker, J. Kim, X. Zhu
  • Anti-resonances and sharp analysis of Maryland localization for all parameters , R. Han, S. Jitomirskaya, and F. Yang
  • Stability of the non-critical 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
  • Anti-resonances 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 ultra-differentiable quasiperiodic cocycles and its spectral applications , H. Cheng, L. Ge, J. You, Q. Zhou

    • 2020
  • Multidimensional Schrödinger Operators Whose Spectrum Features a Half-Line 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 Wang-Casati-Prosen 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 Quasi-Periodic Long-Range Operators on ℓ2(Zd) , L. Ge, J. You and X. Zhao
  • Ballistic Transport for One-Dimensional Quasi-Periodic 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 G-delta 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 multi-frequency quasi-periodic operators on Zd , S. Jitomirskaya, W. Liu
  • Spectral theory of Schrödinger 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
  • Unbounded-Singular 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
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  • W. Liu, D. Ong, Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators. arXiv version
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  • W. Liu, Criteria for embedded eigenvalues for discrete Schrödinger operators. arXiv version
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  • W. Liu, Almost Mathieu operators with completely resonant phases. arXiv version
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  • W. Liu, Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators. arXiv version
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  • W. Liu, The asymptotical behaviour of the embedded eigenvalue for perturbed periodic operators. arXiv version
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  • W. Liu, Absence of singular continuous spectrum for perturbed discrete Schrödinger operators. arXiv version
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  • S. Jitomirskaya, W. Liu, and S. Zhang, Arithmetic spectral transitions. To appear to AMS/PCMI, Harmonic Analysis, 2018 .
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  • Multidimensional Almost-Periodic 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 reflective-hierarchical 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 Bethe-Sommerfeld 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 pseudo-absolute values, W. Liu
  • Sharp bound on the largest positive eigenvalue for one-dimensional Schrodinger operators, W. Liu
  • Upper bounds on the spectral gaps of the quasi-periodic Schrodinger operators with Liouville frequencies, W. Liu and Y. Shi [submitted]
  • Large coupling asymptotics of the Lyapunov exponent for quasi-periodic 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 skew-shifts on higher dimensional tori, R. Han
  • Sch'nol's theorem and the spectrum of long range operators, R. Han
  • Generic continuous spectrum for multi-dimensional quasi periodic Schrodinger operators with rough potentials, Y. Fan, R. Han
  • Full measure reducibility and localization for quasi-periodic 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 non-self-dual 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 Kunz-Souillard Approach to Localization in One Dimension and Applications to Almost-Periodic 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, Qing-Hui Liu, Yan-Hui 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 quasi-periodic 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 quasi-periodic Schrodinger-type 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 Non-Commutative 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 QUASI-PERIODIC LONG RANGE OPERATORS, J. You, S. Zhang, and Q. Zhou
  • Complex one-frequency cocycles, A.Avila, S.Jitomirskaya, C.Sadel
  • On the ground state calculation of a many-body system using a self-consistent basis and quasi-Monte Carlo. An application to water hexamer., I.Georgescu, S.Jitomirskaya, and V. Mandelshtam
  • Bootstrap multiscale analysis and localization for multi-particle continuous Anderson Hamiltonians, A.Klein, S.Nguyen
  • Ground state energy of trimmed discrete Schrödinger 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.Golenishcheva-Kutuzova, 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
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  • Spectral Properties of Schrodinger Operators Arising in the Study of Quasicrystals, D. Damanik, M. Embree, and A. Gorodetski
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  • Continuum Schrodinger Operators Associated With Aperiodic Subshifts, D. Damanik, A. Gorodetski, and J.Fillman
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  • 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. Vandenberg-Rodes
  • Trapping in the random conductance model, A. Vandenberg-Rodes (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 almost-Mathieu 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 quasi-perodic cocycles with singularities and the Lyapunov Exponent of Extended Harper's Model, S. Jitomirskaya and C. Marx
  • Analytic quasi-periodic Schrödinger 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 multi-particle Anderson model , A. Klein, S.Nguyen
  • The Aizenman-Sims-Starr scheme and Parisi formula for mixed p-spin spherical models, W. Chen
  • An approach to chaos in some mixed p-spin 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 , J-M. 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 Sherrington-Kirkpatrick Model with External Field, W. Chen
  • On the Mixed Even-Spin Sherrington-Kirkpatrick 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 Mini-Workshop on Dynamics of Trace Maps and Applications to Spectral Theory (Jan. 16 - 22, 2011), (includes contribution by A. Gorodetski and W. Yessen)