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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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10.1007/s00440-011-0397-9

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1432-2064

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Outliers in the spectrum of iid matrices with boun

Authors: Terence Tao
Publish Date: 2011/11/03
Volume: 155, Issue: 1-2, Pages: 231-263
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Abstract

It is known that if one perturbs a large iid random matrix by a bounded rank error then the majority of the eigenvalues will remain distributed according to the circular law However the bounded rank perturbation may also create one or more outlier eigenvalues We show that if the perturbation is small then the outlier eigenvalues are created next to the outlier eigenvalues of the bounded rank perturbation but if the perturbation is large then many more outliers can be created and their law is governed by the zeroes of a random Laurent series with Gaussian coefficients On the other hand these outliers may be eliminated by enforcing a row sum condition on the final matrix

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Other Papers In This Journal:
  1. Loss without recovery of Gibbsianness during diffusion of continuous spins
  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. Product of random projections, Jacobi ensembles and universality problems arising from free probability
  8. Poincaré type inequalities on the discrete cube and in the CAR algebra
  9. The largest eigenvalue of small rank perturbations of Hermitian random matrices
  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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