3 problems

Let $\rho$ be a probability density with moments of all orders, meaning that … for every $q\geq 1$. Let $E_o\in\mathbb R$. Suppose there is a $\delta>0$ such that, on … the symbol…

Continuity conjecture. The measure $\mu-\mu^{ND}$ is continuous, i.e. it does not charge any point.

Let $d\geq 4$ and let $\mu_{L,E}^0$ be the measures associated with the finite-volume model at energy $E\in(-2d,2d)$. Let $n_d$ denote the density of states of the $d$-dimensional…