{"paper":{"title":"A Note on Discrete Gaussian Combinations of Lattice Vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"cs.CR","authors_text":"Divesh Aggarwal, Oded Regev","submitted_at":"2013-08-11T16:13:31Z","abstract_excerpt":"We analyze the distribution of $\\sum_{i=1}^m v_i \\bx_i$ where $\\bx_1,...,\\bx_m$ are fixed vectors from some lattice $\\cL \\subset \\R^n$ (say $\\Z^n$) and $v_1,...,v_m$ are chosen independently from a discrete Gaussian distribution over $\\Z$. We show that under a natural constraint on $\\bx_1,...,\\bx_m$, if the $v_i$ are chosen from a wide enough Gaussian, the sum is statistically close to a discrete Gaussian over $\\cL$. We also analyze the case of $\\bx_1,...,\\bx_m$ that are themselves chosen from a discrete Gaussian distribution (and fixed).\n  Our results simplify and qualitatively improve upon a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2405","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"}