A law of large numbers for finite-range dependent random matrices

Greg W Anderson; Ofer Zeitouni

doi:10.1002/cpa.20235

A law of large numbers for finite-range dependent random matrices

Greg W Anderson, Ofer Zeitouni

School of Mathematics

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

We consider random Hermitian matrices in which distant above-diagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by combinatorial methods. We also prove that the limit has an algebraic Stieltjes transform by an argument based on dimension theory of Noetherian local rings.

Original language	English (US)
Pages (from-to)	1118-1154
Number of pages	37
Journal	Communications on Pure and Applied Mathematics
Volume	61
Issue number	8
DOIs	https://doi.org/10.1002/cpa.20235
State	Published - Aug 2008

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10.1002/cpa.20235

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A law of large numbers for finite-range dependent random matrices

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