{"paper":{"title":"Eigenvector statistics of the product of Ginibre matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","stat.OT"],"primary_cat":"cond-mat.stat-mech","authors_text":"Bart{\\l}omiej J. Spisak, Pierpaolo Vivo, Zdzis{\\l}aw Burda","submitted_at":"2016-10-28T12:19:47Z","abstract_excerpt":"We develop a method to calculate left-right eigenvector correlations of the product of $m$ independent $N\\times N$ complex Ginibre matrices. For illustration, we present explicit analytical results for the vector overlap for a couple of examples for small $m$ and $N$. We conjecture that the integrated overlap between left and right eigenvectors is given by the formula $O = 1 + (m/2)(N-1)$ and support this conjecture by analytical and numerical calculations. We derive an analytical expression for the limiting correlation density as $N\\rightarrow \\infty$ for the product of Ginibre matrices as we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09184","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"}