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Eigenvector dynamics: theory and some applications

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  • Romain Allez
  • Jean-Philippe Bouchaud

Abstract

We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts, including quantum dissipation (${\bf H}_0$ is then the Hamiltonian) and risk control (in which case ${\bf H}_0$ is the assets return correlation matrix). We specialize our results for the case of a Gaussian Orthogonal ${\bf H}_0$, or when ${\bf H}_0$ is a correlation matrix. We illustrate the usefulness of our framework using financial data.

Suggested Citation

  • Romain Allez & Jean-Philippe Bouchaud, 2011. "Eigenvector dynamics: theory and some applications," Papers 1108.4258, arXiv.org.
  • Handle: RePEc:arx:papers:1108.4258
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    File URL: http://arxiv.org/pdf/1108.4258
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