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Large deviations from freenessMathematical 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