{"paper":{"title":"The rank 1 real Wishart spiked model I. Finite N analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"M. Y. Mo","submitted_at":"2010-11-24T15:56:30Z","abstract_excerpt":"This is the first part of a paper that studies the phase transition in the asymptotic limit of the rank 1 real Wishart spiked model. In this paper, we consider $N$-dimensional real Wishart matrices $S$ in the class $W_{\\mathbb{R}}\\left(\\Sigma,M\\right)$ in which all but one eigenvalues of $\\Sigma$ is $1$. Let the non-trivial eigenvalue of $\\Sigma$ be $1+\\tau$, then as $N$, $M\\rightarrow\\infty$, with $N/M=\\gamma^2$ finite and non-zero, the eigenvalue distribution of $S$ will converge into the Machenko-Pastur distribution inside a bulk region. As $\\tau$ increases from zero, one starts seeing stra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5404","kind":"arxiv","version":1},"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"}