A law of large numbers for finite-range dependent random matrices. (English) Zbl 1189.60018
The paper considers random Hermitian matrices in which distant above-diagonal entries are independent but nearby entries may be correlated. To each random assumed matrix a random band matrix is associated, which has the same limit of empirical distribution of eigenvalues. The limit of the empirical distribution of eigenvalues are found using combinatorial methods. It is also proven that the limit has an algebraic Stieltjes transform. The proof is based on dimension theory of Noetherian local rings. The authors mention a possible application of the theory in the analysis of communication systems, e.g. allowing correlation of the neighbouring antenna pairs in multi-antenna systems.
Reviewer: Cyril Fischer (Praha)
MSC:
| 60B20 | Random matrices (probabilistic aspects) |
| 15B52 | Random matrices (algebraic aspects) |
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 13E05 | Commutative Noetherian rings and modules |
| 43A25 | Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
Keywords:
Hermitian matrices; eigenvalues; combinatorical methods; Stieltjes transform; Noetherian local ringsReferences:
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