10 citations · 19 across the 13 of their papers we have counts for
18 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…
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…
On Simon's Hausdorff Dimension Conjecture
David Damanik, Jake Fillman, Shuzheng Guo +1
Barry Simon conjectured in 2005 that the Szegő matrices, associated with Verblunsky coefficients obeying for…
Ballistic Transport for Periodic Jacobi Operators on
Jake Fillman
In this expository work, we collect some background results and give a short proof of the following theorem: periodic Jacobi matrices on exhibit strong ballistic mot…