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Fluctuations around the semicircle law in free probability theory

Mathematical Physics & Probability

Speaker: Dr. Michael Anshelevich, MSRI
Location: 693 Kerr
Start time: Tue, Jan 9 2001, 4:10PM

The semicircle law is the limit distribution in the free Central Limit theorem. Considering this theorem as a fixed point theorem, the fluctuations around the semicircle law are given by the Chebyshev distributions of the first kind. The result follows from a more dynamic description using the semicircular free convolution semigroup. This description in turn holds for more general free convolution semigroups, in particular the free Poisson (Wishart / Marchenko-Pastur) semigroup.