# Preprints

## 2018

• 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 SchrÃ¶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.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
• 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. 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)