{"paper":{"title":"Completing the picture for the smallest eigenvalue of real Wishart matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-lat","math.MP"],"primary_cat":"math-ph","authors_text":"G. Akemann, M. Kieburg, R. Wegner, T. Guhr, T. Wirtz","submitted_at":"2014-09-01T11:00:10Z","abstract_excerpt":"Rectangular real $N \\times (N + \\nu)$ matrices $W$ with a Gaussian distribution appear very frequently in data analysis, condensed matter physics and quantum field theory. A central question concerns the correlations encoded in the spectral statistics of $WW^T$. The extreme eigenvalues of $W W^T$ are of particular interest. We explicitly compute the distribution and the gap probability of the smallest non-zero eigenvalue in this ensemble, both for arbitrary fixed $N$ and $\\nu$, and in the universal large $N$ limit with $\\nu$ fixed. We uncover an integrable Pfaffian structure valid for all even"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0360","kind":"arxiv","version":3},"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"}