{"paper":{"title":"On a contraction property of Bernoulli canonical processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Rafa{\\l} Martynek, Witold Bednorz","submitted_at":"2018-12-11T14:01:01Z","abstract_excerpt":"In this paper we improve Bernoulli comparison. The result works for independent Rademacher random variables $(\\varepsilon_i)_{i\\geq1}$ and states that we can compare $\\mathbb{E}\\sup_{t\\in T}\\sum_{i\\geq1}\\varphi_{i}(t)\\varepsilon_i$ with $\\mathbb{E}\\sup_{t\\in T}\\sum_{i\\geq1}t_i\\varepsilon_i$, where a function $\\varphi=(\\varphi_i)_{i\\geq1}: \\ell^2\\supset T\\rightarrow\\ell^2$, satisfies certain conditions. Originally, it is assumed that each of $\\varphi_i$ is a contraction. We relax this assumption towards comparison of Gaussian parts of increments, which can be described in the following way. For"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04399","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"}