Dr. Jake Fillman



Visiting Assistant Professor
Virginia Tech

Thesis advisor: David Damanik

A list of my papers on the arxiv

Google Scholar Profile

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:
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.