2 problems

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The two-dimensional localisation and higher-dimensional delocalisation conjecture for the trimmed Anderson model
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…
Conjectureopenanderson-localisation random-schrodinger-operators spectral-theoryarXiv posted 2 days ago
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Spencer's Hölder continuity conjecture for the integrated density of states
Spencer's conjecture. The integrated density of states for the full Hamiltonian should be at least $1/2$ -Hölder continuous.
Conjectureopenanderson-localisation integrated-density-of-states random-operatorsarXiv posted 2 days ago

The two-dimensional localisation and higher-dimensional delocalisation conjecture for the trimmed Anderson model