Eigenvector dynamics under free addition

@article{Allez2014EigenvectorDU,
  title={Eigenvector dynamics under free addition},
  author={Romain Allez and J. Bouchaud},
  journal={arXiv: Probability},
  year={2014},
  volume={03},
  pages={1450010}
}
We investigate the evolution of a given eigenvector of a symmetric (deterministic or random) matrix under the addition of a matrix in the Gaussian orthogonal ensemble. We quantify the overlap between this single vector with the eigenvectors of the initial matrix and identify precisely a "Cauchy flight" regime. In particular, we compute the local density of this vector in the eigenvalues space of the initial matrix. Our results are obtained in a non-perturbative setting and are derived using the… Expand

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References

SHOWING 1-10 OF 25 REFERENCES
Eigenvector dynamics: General theory and some applications.
  • Romain Allez, J. Bouchaud
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
Random matrix theory in semiclassical quantum mechanics of chaotic systems
Eigenvectors of Some Large Sample Covariance Matrices Ensembles
A Brownian motion model for the parameter dependence of matrix elements
A diffusive matrix model for invariant $\beta$-ensembles
Universal correlations for deterministic plus random Hamiltonians.
  • Brézin, Hikami, Zee
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
Invariant beta ensembles and the Gauss-Wigner crossover.
A Brownian‐Motion Model for the Eigenvalues of a Random Matrix
Limit laws for Random matrices and free products
...
1
2
3
...