24 citations · 163 across the 51 of their papers we have counts for
8 papers · 1 filter
Gap Labels for Zeros of the Partition Function of the 1D Ising Model via the Schwartzman Homomorphism
David Damanik, Mark Embree, Jake Fillman
Inspired by the 1995 paper of Baake--Grimm--Pisani, we aim to explain the empirical observation that the distribution of Lee--Yang zeros corresponding to a one-dimensional Ising mo…
Discontinuities of the Integrated Density of States for Laplacians Associated with Penrose and Ammann-Beenker Tilings
David Damanik, Mark Embree, Jake Fillman +1
Aperiodic substitution tilings provide popular models for quasicrystals, materials exhibiting aperiodic order. We study the graph Laplacian associated with four tilings from the mu…
Johnson-Schwartzman Gap Labelling for Ergodic Jacobi Matrices
David Damanik, Jake Fillman, Zhenghe Zhang
We consider two-sided Jacobi matrices whose coefficients are obtained by continuous sampling along the orbits of a homeomorphim of a compact metric space. Given an ergodic probabil…
On Sums of Semibounded Cantor Sets
Jake Fillman, Sara H. Tidwell
Motivated by questions arising in the study of the spectral theory of models of aperiodic order, we investigate sums of functions of semibounded closed subsets of the real line. We…
The Almost Sure Essential Spectrum of the Doubling Map Model is Connected
David Damanik, Jake Fillman
We consider discrete Schrödinger operators on the half line with potentials generated by the doubling map and continuous sampling functions. We show that the essential spectrum of…
Limit-Periodic Dirac Operators with Thin Spectra
Benjamin Eichinger, Jake Fillman, Ethan Gwaltney +1
We prove that limit-periodic Dirac operators generically have spectra of zero Lebesgue measure and that a dense set of them have spectra of zero Hausdorff dimension. The proof comb…
Spectral Characteristics of Schrödinger Operators Generated by Product Systems
David Damanik, Jake Fillman, Philipp Gohlke
We study ergodic Schrödinger operators defined over product dynamical systems in which one factor is periodic and the other factor is either a subshift over a finite alphabet or an…
Gap Labelling for Discrete One-Dimensional Ergodic Schrödinger Operators
David Damanik, Jake Fillman
In this survey, we give an introduction to and proof of the gap labelling theorem for discrete one-dimensional ergodic Schrödinger operators via the Schwartzman homomorphism. To ke…