{"paper":{"title":"A Discrepancy Bound for Deterministic Acceptance-Rejection Samplers Beyond $N^{-1/2}$ in Dimension 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Houying Zhu, Josef Dick","submitted_at":"2015-10-19T04:37:02Z","abstract_excerpt":"In this paper we consider an acceptance-rejection (AR) sampler based on deterministic driver sequences. We prove that the discrepancy of an $N$ element sample set generated in this way is bounded by $\\mathcal{O} (N^{-2/3}\\log N)$, provided that the target density is twice continuously differentiable with non-vanishing curvature and the AR sampler uses the driver sequence $$\\mathcal{K}_M= \\{( j \\alpha, j \\beta ) ~~ mod~~1 \\mid j = 1,\\ldots,M\\}, $$ where $\\alpha,\\beta$ are real algebraic numbers such that $1,\\alpha,\\beta$ is a basis of a number field over $\\mathbb{Q}$ of degree $3$. For the driv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05351","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"}