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Summary: A law of large numbers for finite-range dependent random
matrices
GREG ANDERSON
University of Minnesota
AND
OFER ZEITOUNI
University of Minnesota
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 algebraic Stieltjes transform by an argument based on dimen-
sion theory of noetherian local rings.
c 2000 Wiley Periodicals, Inc.
1 Introduction
Study of the empirical distribution of eigenvalues of random hermitian (or real
symmetric) matrices has a long history, starting with the seminal work of Wigner
[Wig55] and Wishart [Wis28]. Except in cases where the joint distribution of
eigenvalues is explicitly known, most results available are asymptotic in nature and
based on one of the following approaches: (i) the moment method, i. e., evaluation
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