# Eigenvector dynamics under free addition

@article{Allez2014EigenvectorDU,
author={Romain Allez and J. Bouchaud},
journal={arXiv: Probability},
year={2014},
volume={03},
pages={1450010}
}
• Published 2014
• Mathematics, Physics
• arXiv: Probability
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

#### References

SHOWING 1-10 OF 25 REFERENCES
Eigenvector dynamics: General theory and some applications.
• Mathematics, Medicine
• Physical review. E, Statistical, nonlinear, and soft matter physics
• 2012
Universal correlations for deterministic plus random Hamiltonians.
• Brézin, Zee
• Physics, Medicine
• Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
• 1995
Invariant beta ensembles and the Gauss-Wigner crossover.
• Physics, Mathematics
• Physical review letters
• 2012