{"paper":{"title":"Eigenvector dynamics: general theory and some applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-fin.RM","q-fin.ST"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jean-Philippe Bouchaud, Romain Allez","submitted_at":"2012-03-28T11:06:53Z","abstract_excerpt":"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 financial risk control (in which case ${\\bf H}_0$ is the assets return covariance matrix). We argue that the problem can be formulated in terms of the singular values of an overlap matrix, that allows one to define a \"fidelity\" distance. We specialize our results for the case of a Gaussian Or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6228","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}