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Correlations between eigenvalues of large random matrices with independent entries

1995/08/31 by Joseph L. D’Anna, J. D'Anna, A. Zee · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Quantum chaos and dynamical systems #Random Matrices and Applications #cond-mat

paper · pdf · doi:10.1103/physreve.53.1399

23 pages, RevTex, hard figures available from [email protected]

arxiv created 1995/10/09 · openalex publication_date 1996/02/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We derive the connected correlation functions for eigenvalues of large Hermitian random matrices with independently distributed elements using both a diagrammatic and a renormalization-group (RG) inspired approach. With the diagrammatic method we obtain a general form for the one-, two-, and three-point connected Green functions for this class of ensembles when matrix elements are identically distributed, and then discuss the derivation of higher-order functions by the same approach. Using the RG approach we rederive the one- and two-point Green functions and show they are unchanged by choosing certain ensembles with nonidentically distributed elements. Throughout, we compare the Green functions we obtain to those from the class of ensembles with unitary invariant distributions and discuss universality in both ensemble classes. \textcopyright 1996 The American Physical Society.

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