{"paper":{"title":"A Note on Functional Averages over Gaussian Ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.OA"],"primary_cat":"math.PR","authors_text":"Gabriel H. Tucci, Maria V. Vega","submitted_at":"2009-10-03T22:25:09Z","abstract_excerpt":"In this work we find a new formula for matrix averages over the Gaussian ensemble. Let ${\\bf H}$ be an $n\\times n$ Gaussian random matrix with complex, independent, and identically distributed entries of zero mean and unit variance. Given an $n\\times n$ positive definite matrix ${\\bf A}$, and a continuous function $f:\\R^{+}\\to\\R$ such that $\\int_{0}^{\\infty}{e^{-\\alpha t}|f(t)|^2\\,dt}<\\infty$ for every $\\alpha>0$, we find a new formula for the expectation $\\E[\\mathrm{Tr}(f({\\bf HAH^{*}}))]$. Taking $f(x)=\\log(1+x)$ gives another formula for the capacity of the MIMO communication channel, and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0575","kind":"arxiv","version":6},"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"}