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The boundary energy between the two regimes is the mobility edge.","posed_since":"1958","precise":"$H = \\Delta + \\lambda V$ on $\\ell^2(Z^3)$, with $(\\Delta \\psi)(x) = \\sum_{\\left|y-x\\right|=1} \\psi(y)$ the hopping operator (spectrum $[-6, 6]$ at $\\lambda = 0$), $V(x)$ i.i.d. (e.g. uniform on $[-1,1]$), $\\lambda > 0$ small. Prove that there is $E_c(\\lambda)$ such that, almost surely, the spectrum in $\\left|E\\right| > E_c$ is pure point with exponentially decaying eigenfunctions and the spectrum in a nonempty interval inside $\\left|E\\right| < E_c$ is continuous. Answer: a proof.","problem_ref":null,"references":"","settled_by":"A proof of coexistence of localized and delocalized spectrum for one 3D disorder distribution.","status_note":"Localization near band edges is proven; no delocalization result exists on $Z^d$.","title":"Existence of a mobility edge in the 3D Anderson 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