4 problems

A discrete one-dimensional random word model is determined by a word space whose richness controls the exceptional energies excluded from the localization results. Absence-of-excep…

Sharp arithmetic transition conjecture. For (arithmetically) almost every phase, frequency resonances are the only type of resonance that appears. The spectrum is pure point when

Let $d$ be the dimension, let $Omega\subset[0,\infty)^2$ be a simple low-pass spectral shape, and let $N$ be a positive real bandwidth. Define … and let…

Upper-energy conjecture. When the integrability condition on $V$ is dropped, the upper energy $\beta\mathbb{E}[V]$ in the corresponding localization result should be replaced by