Arithmetic localization for quasiperiodic long-range operators with monotone potentials

We study one-dimensional quasiperiodic operators with $α$-Hölder monotone potentials and long-range hopping satisfying $|T(x,y)|\leq \varepsilon e^{-ρ|x-y|}$. Under an explicit smallness condition on $\varepsilon$, we establish uniform Anderson localization for such operators in the regime $ρ>αβ$, w