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

Greg W Anderson, Ofer Zeitouni

Research output: Contribution to journalArticlepeer-review

23 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 languageEnglish (US)
Pages (from-to)1118-1154
Number of pages37
JournalCommunications on Pure and Applied Mathematics
Volume61
Issue number8
DOIs
StatePublished - Aug 2008

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