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BIRS Workshop Lecture Videos

Universality at criticality: Cusp and Circular Edge Cipolloni, Giorgio


In the last decade, Wigner-Dyson-Mehta (WDM) conjecture has been proven for very general random matrix ensembles in the bulk and at the edge of the self consistent density of states (scDos). Recently we proved universality at the cusp of the scDos completing the last remaining case of the WDM conjecture. About universality for non-Hermitian matrices much less is known. The only available result is the proof by Tao and Vu assuming (non-optimal) four moments matching with Ginibre ensemble. In a very recent work we proved universality at the circular edge of any non-Hermitian matrix X with entries i.i.d. real or complex centred random variables without any moment condition.

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