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Large deviations from freeness

Mathematical Physics & Probability

Speaker: Vladislav Kargin, Stanford University
Location: 3106 MSB
Start time: Wed, Oct 27 2010, 4:10PM

Let H=A+UBU* where A and B are two N-by-N Hermitian matrices and U is a Haar-distributed random unitary matrix, and let μ_H, μ_A, and μ_B be empirical measures of eigenvalues of matrices H, A, and B, respectively. Then, it is known that for large N, measure μ_H is close to the free convolution of measures μ_A and μ_B, where the free convolution is a non-linear operation on probability measures. The large deviations of the cumulative distribution function of μ_H from its expectation have been studied by Chatterjee who derived an exponential estimate on the probability of the large deviation with the rate which is sublinear in N, that is, P