Large deviations of the maximum eigenvalue in Wishart random matrices
نویسندگان
چکیده
منابع مشابه
Large deviations of the maximum eigenvalue for wishart and Gaussian random matrices.
We present a Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this probability is computed explicitly for Wishart and Gaussian ensembles. The method is general and applies to other related problems, e.g., the joint large deviation func...
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Using a change-of-measure argument, we prove an equality in law between the process of largest eigenvalues in a generalized Wishart random-matrix process and a last-passage percolation process. This equality in law was conjectured by Borodin and Péché (2008).
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Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M dagger M where M is a complex matrix drawn from a normalized distribution P(M) approximately exp(-Tr [AMB M dagger]) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called correlated Wishart matrices occur in many fields ranging from information theo...
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Again, this can be viewed as a change of variables; on the left-hand side, there are n diagonal free parameters wjj and n(n−1) 2 off-diagonal free parameters wjk, j < k in the matrix W (the remaining offdiagonal parameters are fixed, as W is symmetric); on the right-hand side, there are n free parameters in the matrix Λ and (n − 1) + (n − 2) + . . . + 1 + 0 = n(n−1) 2 free parameters in the mat...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2007
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/40/16/005