Rising GUE process from fixed level converges in polylog time to extended semi-discrete sine kernel, enabling bulk universality for Wigner matrices with near-optimal moments without DBM.
Ramírez, Benjamin Schlein, and Horng-Tzer Yau,Bulk universality for Wigner matrices, Comm
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Rising GUE Eigenvalue Process from a Fixed Level
Rising GUE process from fixed level converges in polylog time to extended semi-discrete sine kernel, enabling bulk universality for Wigner matrices with near-optimal moments without DBM.