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03:30 PM - 05:00 PM
959 Evans |
Student Probability/PDE Seminar, More on exclusion processes and entropy inequalities, Alan Hammond, UC Berkeley
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03:30 PM - 05:00 PM
443 Evans |
Random Matrices & Asymptotical Combinatorics Seminar, Semicircle-type Laws: the method of moments in a new setting, Ioana Dumitriu, UC Berkeley
As the size of the matrix tends to infinity, the level density of a Gaussian ensemble (more generally, Wigner ensemble) tends to the semicircle distribution. This can be shown by the method of moments. For the Wishart ensembles, similar results hold, with the limiting distribution depending on a parameter gamma which is the ratio of the two dimensions of the matrix.
I will show this result in a more general beta setting, for both the Hermite and the Laguerre ensembles, and generalize to slightly more complicated random matrices which can be modeled in a "fixed plus Gaussian" setting.
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