Titlebook: Introduction to Random Matrices; Theory and Practice Giacomo Livan,Marcel Novaes,Pierpaolo Vivo Book 2018 The Author(s) 2018 Coulomb Gas Ap

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Resolve(nt) the Semicircle,In this Chapter, we introduce the so called ., a complex function from which the spectral density can be calculated.

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Finite ,,Look back at Chap.?., where we constructed Gaussian matrices and histogrammed their eigenvalues.

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,Meet Andréief,In this Chapter, we present a couple of very useful integral identities involving the Vandermonde determinant, and one cute application.

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Finite , Is Not Finished,In this short Chapter, we compute in the quickest way the spectral density for the GOE (.) and GSE (.).

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Classical Ensembles: Wishart-Laguerre,In this Chapter, we present one of the “classical” examples of rotationally invariant models: the Wishart-Laguerre (WL) ensemble.

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Replicas for GOE,In this Chapter, we apply the Edwards-Jones formula to compute the average spectral density of the GOE ensemble.

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