5 problems

Let a continuous random Schrödinger operator act on $L^2(\mathbb{R})$, and let $E_0$ be the bottom of its spectrum. Its integrated density of states is denoted by $N(E)$. Lifshitz'…

Sabot–Tarrès–Zeng conjecture. The asymptotic behavior of the IDS of $H_\beta$ does not exhibit Lifshitz tails.

Let $N_\lambda(E)$ denote the integrated density of states of the Anderson model on the Bethe lattice, and suppose that the random variables are bounded and non-negative,…

Leading-asymptotics conjecture. The leading term is conjectured to satisfy

Consider the one-dimensional Bernoulli displacement model with coupling parameter $\lambda$, integrated density of states $N$, and almost-sure spectrum $\Sigma_{\lambda}$. For…