3 problems

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Bellissard's semicircle-law conjecture for higher-dimensional effective Hamiltonians
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…
Conjectureopenanderson-model random-matrices semicircle-lawarXiv posted 2 days ago
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Conjecture that the semicircle law holds without the variance assumption
Let ${\bf X}_n$ be a sequence of random matrices satisfying the martingale and variance conditions in the paper, except possibly assumption … , and respectively Theorem … ; in part…
Conjectureopendependent-random-variables random-matrices semicircle-lawarXiv posted 3 days ago
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The semicircle law conjecture for sparse random regular graphs
The semicircle law conjecture. If $d\rightarrow\infty$ , then the empirical spectral distribution of $\frac{1}{\sqrt n}M'_n$ converges to the standard semicircle distribution. This…
Conjecturesolvedrandom-regular-graphs semicircle-law spectral-graph-theoryarXiv posted 3 days ago

Bellissard's semicircle-law conjecture for higher-dimensional effective Hamiltonians