A law of large numbers for finite-range dependent random matrices
Abstract
Description
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.
26 pages, LaTeX Revision includes additional results on consequences of algebracity of Stieltjes transform
26 pages, LaTeX Revision includes additional results on consequences of algebracity of Stieltjes transform