{"paper":{"title":"Almost sure localization of the eigenvalues in a gaussian information plus noise model. Applications to the spiked models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pascal Vallet, Philippe Loubaton","submitted_at":"2010-09-29T08:47:25Z","abstract_excerpt":"Let $\\boldsymbol{\\Sigma}_N$ be a $M \\times N$ random matrix defined by $\\boldsymbol{\\Sigma}_N = \\mathbf{B}_N + \\sigma \\mathbf{W}_N$ where $\\mathbf{B}_N$ is a uniformly bounded deterministic matrix and where $\\mathbf{W}_N$ is an independent identically distributed complex Gaussian matrix with zero mean and variance $\\frac{1}{N}$ entries. The purpose of this paper is to study the almost sure location of the eigenvalues $\\hat{\\lambda}_{1,N} \\geq ... \\geq \\hat{\\lambda}_{M,N}$ of the Gram matrix ${\\boldsymbol \\Sigma}_N {\\boldsymbol \\Sigma}_N^*$ when $M$ and $N$ converge to $+\\infty$ such that the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5807","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"}