Seminário das Sextas - Random Matrices, Graphs and a combinatorial proof of Wigner's Semi-Circle Law

In this seminar, we present a combinatorial proof of Wigner's Semi-Circle Law, a fundamental result in random matrix theory. It describes the limiting behavior of the eigenvalue distribution of large Gaussian Orthogonal Ensemble (GOE) matrices. While the original proof of the Semi-Circle Law relies on advanced techniques from analysis, our approach provides an alternative perspective through combinatorial methods.

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