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

By Greg W. Anderson, Ofer Zeitouni. 2006

56 citations recorded by the source corpus.

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. © 2008 Wiley Periodicals, Inc.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/76070c84541593a39bffbae2a3a711be13b43d26

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Statistics and Probability

Citations in the corpus

THE SPECTRUM OF RANDOM INNER-PRODUCT KERNEL MATRICES (2012, background): “For example, the spectral distribution of random matrices with “finite-range” dependency among entries is studied in [3].”
Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half‐Plane (2015, background): “4 of [8] shows that the Stieltjes transformm.”
Fluctuations of eigenvalues and second order Poincaré inequalities (2007, result): “The recent works of Anderson and Zeitouni [ 2 ], Dumitriu and Edelman [22], Rider and Silverstein [44], Rider and Vir´ag [43], Jiang [32], and Hachem et. al. [28, 29] provide several illuminating insights and new results.”
On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries (2011, unknown): “On the other hand Anderson and Zeitouni [4] constructed models of random matrices with locally dependent entries for which the limiting spectral distribution is different from that of classical random matrices.”