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

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

2006-09-13

arxiv.org/abs/math/0609364v2

Mathematics

Probability

26 pages, LaTeX Revision includes additional results on consequences of algebracity of Stieltjes transform

Scientific paper

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
dimension theory of noetherian local rings.

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