10 problems

Let $H(g)$ be a $\Gamma$-trimmed random Schrödinger operator on $\mathbb{Z}^d$ satisfying the Assumptions. Suppose that the complement of $\Gamma$ is a union of finite connected co…

Borderline Lifshits-tail conjecture. As $E\downarrow0$,

Let $N(\lambda)$ be the eigenvalue counting function of the Schrödinger operator considered in the paper, and define … Here $\kappa$ is the parameter appearing in the model. The ei…

Let $H$ be the Schrödinger operator considered in the paper, let $N(\lambda)$ be its eigenvalue counting function, and let $R_{\mathrm h}(\lambda)$ denote the half-line hyperunifor…

White-noise semigroup variance conjecture. One has

Higher-eigenvalue Airy-process conjecture. For any fixed $k$, as $n\to\infty$, the tuple $(\alpha_{n,1},\ldots,\alpha_{n,k})$ converges in distribution to the top $k$ points of the…

Let $G_n$ be the hexagonal-lattice rhombus with $2n-1$ levels, and let $H_n$ be its weighted adjacency operator. In the i.i.d. model, all edge weights are independent copies of a n…

Let $E$ be distributed according to the arcsine law, $U$ be uniform on $[0,1]$, and let $\mathcal{Z}$ be a standard two-sided Brownian motion started from $0$, independent of $E$ a…

Let $H(g)$ be the trimmed Anderson random Schrödinger operator in dimension $d$, let $H_\Gamma$ be the associated periodic operator, and let $I$ be an interval contained in the abs…

Let $H_\omega$ be the two-dimensional discrete random Schrödinger operator … on $l^2(\mathbb{Z}^2)$, where the independent random variables $\omega_i$ are uniformly distributed in…