{"paper":{"title":"Norms of weighted sums of log-concave random vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.MG","authors_text":"Apostolos Giannopoulos, Giorgos Chasapis, Nikos Skarmogiannis","submitted_at":"2019-06-09T21:44:21Z","abstract_excerpt":"Let $C$ and $K$ be centrally symmetric convex bodies of volume $1$ in ${\\mathbb R}^n$. We provide upper bounds for the multi-integral expression \\begin{equation*}\\|{\\bf t}\\|_{C^s,K}=\\int_{C}\\cdots\\int_{C}\\Big\\|\\sum_{j=1}^st_jx_j\\Big\\|_K\\,dx_1\\cdots dx_s\\end{equation*} in the case where $C$ is isotropic. Our approach provides an alternative proof of the sharp lower bound, due to Gluskin and V. Milman, for this quantity. We also present some applications to \"randomized\" vector balancing problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03719","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"}