Abstract
We compute the limiting eigenvalue statistics at the edge of the spectrum of large Hermitian random matrices perturbed by the addition of small rank deterministic matrices. We consider random Hermitian matrices with independent Gaussian entries M
ij
,i≤j with various expectations. We prove that the largest eigenvalue of such random matrices exhibits, in the large N limit, various limiting distributions depending on both the eigenvalues of the matrix
and its rank. This rank is also allowed to increase with N in some restricted way.
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An erratum to this article is available at http://dx.doi.org/10.1007/s00440-005-0480-1.
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Péché, S. The largest eigenvalue of small rank perturbations of Hermitian random matrices. Probab. Theory Relat. Fields 134, 127–173 (2006). https://doi.org/10.1007/s00440-005-0466-z
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DOI: https://doi.org/10.1007/s00440-005-0466-z
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Random Matrice
- Large Eigenvalue