7 problems

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…

Let $H_{\lambda}$ be the Anderson Hamiltonian on a Bethe lattice, with bounded random potential having a sufficiently regular probability distribution, and let $L_{\lambda}(E)$ den…

Let $H_{\lambda}$ be the Anderson Hamiltonian on a Bethe lattice of branching number $K$, with disorder parameter $\lambda$. The free operator has an $l^{2}$ spectral threshold at…

Band-center singularity conjecture. As $E\to 0$,

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