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Title of Journal: Probab Theory Relat Fields

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Abbravation: Probability Theory and Related Fields

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Springer-Verlag

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DOI

10.1007/s11095-014-1452-x

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1432-2064

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The largest eigenvalue of small rank perturbations

Authors: S Péché
Publish Date: 2005/08/17
Volume: 134, Issue: 1, Pages: 127-173
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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 Open image in new window and its rank This rank is also allowed to increase with N in some restricted way

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  2. On the Dirichlet problem for asymmetric zero-range process on increasing domains
  3. Propagation and conditional propagation of chaos for pressureless gas equations
  4. Wasserstein space over the Wiener space
  5. Markov processes on partitions
  6. Quasi-stationary distributions for structured birth and death processes with mutations
  7. Outliers in the spectrum of iid matrices with bounded rank perturbations
  8. Product of random projections, Jacobi ensembles and universality problems arising from free probability
  9. Poincaré type inequalities on the discrete cube and in the CAR algebra
  10. Invariance principle for the random conductance model
  11. Modified logarithmic Sobolev inequalities and transportation inequalities
  12. Asymptotic statistical equivalence for scalar ergodic diffusions
  13. Zero-temperature Glauber dynamics on $${\mathbb{Z}^d}$$
  14. Selector processes on classes of sets
  15. The divergence of Banach space valued random variables on Wiener space
  16. A simple proof of exponential decay of subcritical contact processes
  17. Large deviations for many Brownian bridges with symmetrised initial-terminal condition
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