{"paper":{"title":"$L^p$ bounds for a central limit theorem with involutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Subhankar Ghosh","submitted_at":"2009-05-08T00:08:34Z","abstract_excerpt":"Let $E=((e_{ij}))_{n\\times n}$ be a fixed array of real numbers such that $e_{ij}=e_{ji}, e_{ii}=0$ for $1\\le i,j \\le n$. Let the permutation group be denoted by $S_n$ and the collection of involutions with no fixed points by $\\Pi_n$, that is, $\\Pi_n=\\{\\pi\\in S_n: \\pi^2= id, \\pi(i)\\neq i\\,\\forall i\\}$ with id denoting the identity permutation. For $\\pi$ uniformly chosen from $\\Pi_n$, let $Y_E=\\sum_{i=1}^n e_{i\\pi(i)}$ and $W=(Y_E-\\mu_E)/\\sigma_E$ where $\\mu_E=E(Y_E)$ and $\\sigma_E^2= Var(Y_E)$. Denoting by $F_W$ and $\\Phi$ the distribution functions of $W$ and a $\\mathcal{N}(0,1)$ variate resp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.1150","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"}