Dr. Jake Fillman

Assistant Professor

Texas State University

Thesis advisor: David Damanik

A list of my papers on the arxiv

Google Scholar Profile

ORCID Identifier 0000-0003-4716-710X


Work supported in part by:
AMS-Simons Travel Grant: 2016-2018
Simons Collaboration Grant: 2020-2025


Books:

David Damanik, Jake Fillman
One-Dimensional Ergodic Schrödinger Operators, I: General Theory. Submitted
One-Dimensional Ergodic Schrödinger Operators, II: Specific Classes. In progress.


Submitted Papers:

Jon Chaika, David Damanik, Jake Fillman, Philipp Gohlke
Zero-measure spectrum for multi-frequency Schrödinger operators
[arxiv]


Accepted Papers:

Michael Boshernitzan, David Damanik, Jake Fillman, Milivoje Lukic
Ergodic Schrödinger operators in the infinite-measure setting
To appear in Journal of Spectral Theory
[arxiv]


Published Papers:

David Damanik, Jake Fillman, Anton Gorodetski
Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set
Journal of Functional Analysis 280 (2021), no. 7, 108911.
[arxiv]


David Damanik, Jake Fillman, Mark Helman, Jacob Kesten, Selim Sukhtaiev
Random Hamiltonians with arbitrary point interactions
Journal of Differential Equations 282 (2021), 104-126.
[arxiv]


David Damanik, Jake Fillman, Selim Sukhtaiev
Localization for Anderson models on metric and discrete tree graphs
Mathematische Annalen 376 (2020), 1337–1393.
[
arxiv ] [ journal ] [ MathSciNet ]


Jake Fillman, Rui Han
Discrete Bethe–Sommerfeld conjecture for triangular, square, and hexagonal lattices
Journal d'Analyse Mathématique 142 (2020), no. 1, 271-321.
[arxiv]


Christopher Cedzich, Jake Fillman, Tobias Geib, Albert Werner
Singular continuous Cantor spectrum for magnetic quantum walks
Letters in Mathematical Physics 110 (2020), 1141-1158.
[
arxiv ] [ journal ] [MathSciNet]


Mark Embree, Jake Fillman
Spectra of discrete two-dimensional periodic Schrödinger operators with small potentials
Journal of Spectral Theory 9 (2019), no. 3,1063–1087.
[
arxiv ] [ journal ] [ MathSciNet ]


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
Transactions of the American Mathematical Society 372 (2019), no. 5, 3619–3667.
[
arxiv ] [ journal ] [ MathSciNet ]


Valmir Bucaj, David Damanik, Jake Fillman, Vitaly Gerbuz, Tom VandenBoom, Fengpeng Wang, Zhenghe Zhang
Positive Lyapunov exponents and a large deviation theorem for continuum Anderson models, briefly
Journal of Functional Analysis 277 (2019), no. 9, 3179–3186.
[
arxiv ] [ journal ] [ MathSciNet ]


David Damanik, Jake Fillman, Anton Gorodetski
Multidimensional almost-periodic Schrödinger operators with Cantor spectrum
Annales Henri Poincaré 20 (2019), no. 4, 1393–1402.
[
arxiv ] [ journal ] [ MathSciNet ]


David Damanik, Jake Fillman
Limit-periodic Schrödinger operators with Lipschitz continuous IDS
Proceedings of the American Mathematical Society 147 (2019), no. 4, 1531–1539.
[
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), no. 1, 132–147.
[
arxiv ] [ journal ] [ MathSciNet ]


Jake Fillman, May Mei
Spectral properties of continuum Fibonacci Schrödinger operators
Annales Henri Poincaré 19 (2018), no. 1, 237–247.
[
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), no. 2, 571–580.
[
arxiv ] [ journal ] [ MathSciNet ]


Jake Fillman, Darren Ong, Zhenghe Zhang
Spectral characteristics of the unitary critical almost-Mathieu operator
Communications in Mathematical Physics 351 (2017), no. 2, 525–561.
[
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), no. 3, 1275–1297.
[
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), no. 4, 1101–1118.
[
arxiv ] [ journal ] [ MathSciNet ]


Jake Fillman, Milivoje Lukic
Spectral homogeneity of limit-periodic Schrödinger operators
Journal of Spectral Theory 7 (2017), no. 2, 387–406.
[
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), no. 12, 5107–5143.
[
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), no. 1, 225–239.
[
arxiv ] [ journal ] [ MathSciNet ]


Jake Fillman
Spectral homogeneity of discrete one-dimensional limit-periodic operators
Journal of Spectral Theory 7 (2017), no. 1, 201–226.
[
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 (9) 105 (2016), no. 3, 293–341.
[
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.
[
arxiv ] [ journal ] [ MathSciNet ]


Jake Fillman, Yuki Takahashi, William Yessen
Mixed spectral regimes for square Fibonacci Hamiltonians
Journal of Fractal Geometry , 3 (2016), no. 4, 377–405.
[
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), no. 4, 1009–1023.
[
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), no. 16, 7110–7129.
[
arxiv ] [ journal ] [ MathSciNet ]


Charles Puelz, Mark Embree, and Jake Fillman
Spectral approximation for quasiperiodic Jacobi operators
Integral Equations and Operator Theory 82 (2015), no. 4, 533–554.
[
arxiv ] [ journal ] [ MathSciNet ]


David Damanik, Jake Fillman, and Robert Vance
Dynamics of unitary operators
Journal of Fractal Geometry 1 (2014), no. 4, 391–425.
[
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
[ arxiv ] [ journal ] [ MathSciNet ]


Expository Writing:

David Damanik, Jake Fillman, Shuzheng Guo, and Darren Ong
On Simon's Hausdorff dimension conjecture
[arxiv]


Jake Fillman
Ballistic transport for periodic Jacobi operators on Z^d
[arxiv]


David Damanik, Jake Fillman
Schrodinger operators with thin spectra
IAMP News Bulletin
[link]


David Damanik, Jake Fillman
Spectral properties of limit-periodic operators
In: Analysis and Geometry on Graphs and Manifolds (eds. Matthias Keller, Daniel Lenz, and Radoslaw Wojciechowski)
[arxiv]


Jake Fillman, Tom VandenBoom
A surprising connection between quantum mechanics and shallow water waves
Snapshots of Modern Mathematics from Oberwolfach
[link]


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