# Dr. Jake Fillman

## Visiting Assistant Professor Virginia Tech

A list of my papers on the arxiv

ORCID Identifier 0000-0003-4716-710X

Accepted Papers:

 [abstract] [arxiv] David Damanik, Jake Fillman Limit-periodic Schrödinger operators with Lipschitz continuous IDS To appear in Proceedings of the American Mathematical Society [abstract] [arxiv] Mark Embree, Jake Fillman Spectra of discrete two-dimensional periodic Schrödinger operators with small potentials To appear in Journal of Spectral Theory

Submitted Papers:

 [abstract] [arxiv] David Damanik, Jake Fillman, Anton Gorodetski Multidimensional almost-periodic Schrödinger operators with Cantor spectrum [abstract] [arxiv] Jake Fillman, Rui Han Discrete Bethe–Sommerfeld conjecture for triangular, square, and hexagonal lattices [abstract] [arxiv] David Damanik, Jake Fillman Spectral properties of limit-periodic operators [abstract] [arxiv] Valmir Bucaj, David Damanik, Jake Fillman, Vitaly Gerbuz, Tom VandenBoom, Fengpeng Wang, Zhenghe Zhang Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent

Published Papers:

 [abstract] [arxiv] [journal] [MathSciNet] Jake Fillman, Darren Ong, Tom VandenBoom Spectral approximation for ergodic CMV matrices with an application to quantum walks Journal of Mathematical Analysis and Applications 467 (2018), 132–147. [abstract] [arxiv] [journal] [MathSciNet] Jake Fillman, May Mei Spectral properties of continuum Fibonacci Schrödinger operators Annales Henri Poincaré 19 (2018), 237–247. [abstract] [arxiv] [journal] [MathSciNet] Jake Fillman, Darren Ong A condition for purely absolutely continuous spectrum for CMV operators using the density of states Proceedings of the American Mathematical Society 146 (2018), 571–580. [abstract] [arxiv] [journal] [MathSciNet] Jake Fillman, Darren Ong, Zhenghe Zhang Spectral characteristics of the unitary critical almost-Mathieu operator Communications in Mathematical Physics 351 (2017), 525–561. [abstract] [arxiv] [journal] [MathSciNet] Jake Fillman Ballistic transport for limit-periodic Jacobi matrices with applications to quantum many-body problems Communications in Mathematical Physics 350 (2017), 1275–1297. [abstract] [arxiv] [journal] [MathSciNet] David Damanik, Jake Fillman, Milivoje Lukic Limit-periodic continuum Schrödinger operators with zero-measure Cantor spectrum Journal of Spectral Theory 7 (2017), 1101–1118. [abstract] [arxiv] [journal] [MathSciNet] Jake Fillman, Milivoje Lukic Spectral homogeneity of limit-periodic Schrödinger operators Journal of Spectral Theory 7 (2017), 387–406. [abstract] [arxiv] [journal] [MathSciNet] Jake Fillman, Darren Ong Purely singular continuous spectrum for limit-periodic CMV operators with applications to quantum walks Journal of Functional Analysis 272 (2017), 5107–5143. [abstract] [arxiv] [journal] [MathSciNet] Jake Fillman Purely singular continuous spectrum for Sturmian CMV matrices via strengthened Gordon Lemmas Proceedings of the American Mathematical Society 145 (2017), 225–239. [abstract] [arxiv] [journal] [MathSciNet] Jake Fillman Spectral homogeneity of discrete one-dimensional limit-periodic operators Journal of Spectral Theory 7 (2017), 201–226. [abstract] [arxiv] [journal] [MathSciNet] David Damanik, Jake Fillman, and Darren Ong Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices Journal de Mathématiques Pures et Appliquées 105 (2016), 293–341. [abstract] [arxiv] [journal] [MathSciNet] David Damanik, Jon Erickson, Jake Fillman, Gerhardt Hinkle, and Alan Vu Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line Journal of Approximation Theory 208 (2016), 59–84. [abstract] [arxiv] [journal] [MathSciNet] Jake Fillman, Yuki Takahashi, William Yessen Mixed spectral regimes for square Fibonacci Hamiltonians Journal of Fractal Geometry, 3 (2016), 377–405. [abstract] [arxiv] [journal] [MathSciNet] David Damanik, Jake Fillman, Milivoje Lukic, and William Yessen Characterizations of uniform hyperbolicity and spectra of CMV matrices Discrete and Continuous Dynamical Systems – Series S 9 (2016), 1009–1023. [abstract] [arxiv] [journal] [MathSciNet] David Damanik, Jake Fillman, Milivoje Lukic, and William Yessen Uniform hyperbolicity for Szegő cocycles and applications to random CMV matrices and the Ising model International Mathematics Research Notices 2015 (2015), 7110–7129. [abstract] [arxiv] [journal] [MathSciNet] Charles Puelz, Mark Embree, and Jake Fillman Spectral approximation for quasiperiodic Jacobi operators Integral Equations and Operator Theory 82 (2015), 533–554. [abstract] [arxiv] [journal] [MathSciNet] David Damanik, Jake Fillman, and Robert Vance Dynamics of unitary operators Journal of Fractal Geometry 1 (2014), 391–425. [abstract] [arxiv] [journal] [MathSciNet] David Damanik, Jake Fillman, and Anton Gorodetski Continuum Schrödinger operators associated with aperiodic subshifts Annales Henri Poincaré 15 (2014), 1123–1144. *This paper was awarded the 2014 Annales Henri Poincaré Prize
Book:
• Spectral Theory of Discrete One-Dimensional Ergodic Schrödinger Operators, with David Damanik (In preparation)
Papers in Proceedings Volumes:

 [abstract] [arxiv] [journal] Jake Fillman Resolvent methods for quantum walks with an application to a Thue-Morse quantum walk Interdisciplinary Information Sciences 23 (2017), 27–32.