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Universality for Wigner random matrices

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Wigner random matrices are a basic example of a Hermitian random matrix model, in which the upper-triangular entries are jointly independent. The most famous example of a Wigner random matrix is the Gaussian Unitary Ensemble (GUE), which is particularly amenable to study due to its rich algebraic structure. In particular, the fine-scale distribution of the eigenvalues is completely understood. There has been much recent progress on extending these distribution laws to more general Wigner matrices, a phenomenon sometimes referred to as universality. In this talk we will discuss recent work of Van Vu and myself on establishing several cases of this universality phenomenon, as well as parallel work of Erdos, Schlein, and Yau.

This talk is part of the Rouse Ball Lectures series.

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