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• W2136341714 abstract "Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in question. In this article we attempt to formulate a unified technique for deriving such results via relatively soft arguments. In the process, we introduce a notion of ‘second order Poincaré inequalities’: just as ordinary Poincaré inequalities give variance bounds, second order Poincaré inequalities give central limit theorems. The proof of the main result employs Stein’s method of normal approximation. A number of examples are worked out, some of which are new. One of the new results is a CLT for the spectrum of gaussian Toeplitz matrices." @default.
• W2136341714 created "2016-06-24" @default.
• W2136341714 creator A5025655425 @default.
• W2136341714 date "2007-11-30" @default.
• W2136341714 modified "2023-09-25" @default.
• W2136341714 title "Fluctuations of eigenvalues and second order Poincaré inequalities" @default.
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• W2136341714 doi "https://doi.org/10.1007/s00440-007-0118-6" @default.
• W2136341714 hasPublicationYear "2007" @default.
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