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Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices

Student-Run Applied & Math Seminar

Speaker: Sean O'Rourke, UC Davis
Location: 2112 MSB
Start time: Wed, Oct 28 2009, 12:10PM

Large dimensional random matrices, specifically Wigner matrices, have been applied to a variety of fields including physics and mathematics. The prototypical examples of Wigner matrices are the the Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE), and Gaussian symplectic ensemble (GSE). This talk will be centered around studying the eigenvalues in the bulk for these three Gaussian ensembles. We will explain a result due to Gustavsson which states that the fluctuation of eigenvalues in the bulk for the GUE are normally distributed in the limit. Time-permitting, we will discuss how Gustavsson's result can be extended to the GOE and GSE.