{"paper":{"title":"Tails of Random Matrix Diagonal Elements: The Case of the Wishart Inverse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.IT"],"primary_cat":"cs.IT","authors_text":"Aris L. Moustakas","submitted_at":"2011-04-11T11:27:22Z","abstract_excerpt":"We analytically compute the large-deviation probability of a diagonal matrix element of two cases of random matrices, namely $\\beta=[\\vec H^\\dagger\\vec H]^{-1}_{11}$ and $\\gamma=[\\vec I_N+\\rho\\vec H^\\dagger\\vec H]^{-1}_{11}$, where $\\vec H$ is a $M\\times N$ complex Gaussian matrix with independent entries and $M\\geq N$. These diagonal entries are related to the \"signal to interference and noise ratio\" (SINR) in multi-antenna communications. They depend not only on the eigenvalues but also on the corresponding eigenfunction weights, which we are able to evaluate on average constrained on the va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1910","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"}