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Local semicircle law at the edge of spectrum for Gaussian $\beta$-ensembles

Ergodic Theory & Statistical Mechanics

Local semicircle law at the edge of spectrum for Gaussian $\beta$-ensembles

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Percy Wong, Princeton University
Fine Hall 801

We prove, via the moments method, a local semicircle law for the Gaussian $\beta$-ensembles at the almost optimal scaling of $n^{-2/3 +\epsilon}$ at the edge of the spectrum for all $\beta \geq 1$.