16 problems

Let $H$ be the Anderson model in dimension $d=2$. Two-dimensional Anderson localization conjecture. The spectrum of $H$ is pure point with dynamically localized eigenfunctions. Thi…

Let a regular tree be given, let a finite graph be given, and consider the Anderson model obtained by adding a random potential to the Laplace operator on their product. The spectr…

Let $X_n$ be the random matrices arising as effective Hamiltonians in dimensions higher than two, in the class of correlated ensembles considered in the paper, and let the density…

Consider the Anderson Hamiltonian … on $\ell^2(\mathbb Z^d)$, where $\lambda>0$ is the coupling constant and $V_{\omega}$ is an i.i.d. random potential. For sufficiently large coup…

Let $H=-\Delta+\delta V$ be the $d$-dimensional Anderson model on $\ell^2(\mathbb{Z}^d)$, where $\Delta$ is the lattice Laplacian, $V$ is a random potential with independent identi…

Consider the Anderson model in dimensions $d\geqslant 3$, with energy used to distinguish its eigenstates. A mobility edge is a threshold energy separating delocalized and localize…

Let $p$ be the Bernoulli parameter, let $\beta^{-1}(n)$ denote the decreasing sequence appearing in the model, and let $I_{p,\zeta}(x)$ be the integrated density of states at disor…

Let $H$ be the multi-dimensional Anderson Hamiltonian, with dimension $d\geq 3$. At sufficiently low energies, the extended-states conjecture. $H$ has extended states; equivalently…

Consider the Anderson model on the lattice $\mathds{Z}^d$ at small disorder, and let its spectrum be studied almost surely with respect to the random potential. Spectral-type conje…

Consider the one-dimensional Anderson model with independent site variables taking the two values $0$ and $1$, and with sufficiently small disorder. Let Proposition 4 denote the Po…

Let $H_\lambda$ be the Anderson model on the Bethe lattice, with disorder strength $\lambda$, and let $\Sigma_\lambda$ be its almost-sure spectrum. The small-disorder pure ac spect…

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,…

Let $H_\lambda$ be the Anderson Hamiltonian on the Bethe lattice, with disorder strength $\lambda>0$. If transport occurs and its transport index $\alpha\in(0,1]$ is defined by the…

Consider the Anderson model, a random Schrödinger operator on a regular square lattice in dimension three or higher, restricted to a finite box, with random diagonal entries and de…

Let the one-dimensional Anderson model have eigenvalues (EVs), and let $I$ be an interval. Poisson statistics conjecture. The distribution of the distances between eigenvalues come…

Let $\Xi_0$ be the set of chemical potentials for which the zero-temperature conductivity measure and in-phase linear-response current have been constructed, and let…