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dc.contributor.authorAllez, Romain
dc.contributor.authorBouchaud, Jean-Philippe
dc.date.accessioned2013-01-29T14:00:54Z
dc.date.available2013-01-29T14:00:54Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10916
dc.language.isoenen
dc.subjectStatistical Financeen
dc.subjectRisk Managementen
dc.subjectProbabilityen
dc.subjectStatistical Mechanicsen
dc.subject.ddc519en
dc.subject.classificationjelG1en
dc.titleEigenvector dynamics: General theory and some applicationsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe propose a general framework to study the stability of the subspace spanned by P consecutive eigenvectors of a generic symmetric matrix H0 when a small perturbation is added. This problem is relevant in various contexts, including quantum dissipation (H0 is then the Hamiltonian) and financial risk control (in which case H0 is the assets' return covariance matrix). We argue that the problem can be formulated in terms of the singular values of an overlap matrix, which allows one to define an overlap distance. We specialize our results for the case of a Gaussian orthogonal H0, for which the full spectrum of singular values can be explicitly computed. We also consider the case when H0 is a covariance matrix and illustrate the usefulness of our results using financial data. The special case where the top eigenvalue is much larger than all the other ones can be investigated in full detail. In particular, the dynamics of the angle made by the top eigenvector and its true direction defines an interesting class of random processes.en
dc.relation.isversionofjnlnamePhysical Review. E, Statistical, Nonlinear, and Soft Matter Physics
dc.relation.isversionofjnlvol86en
dc.relation.isversionofjnlissue4en
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpagesn°046202en
dc.relation.isversionofdoihttp://dx.doi.org/10.1103/PhysRevE.86.046202en
dc.identifier.urlsitehttp://arxiv.org/abs/1203.6228v2en
dc.relation.isversionofjnlpublisherAmerican Physical Societyen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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