{"paper":{"title":"Upper Tail Estimates with Combinatorial Proofs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jan H\\k{a}z{\\l}a, Thomas Holenstein","submitted_at":"2014-05-09T20:29:00Z","abstract_excerpt":"We study generalisations of a simple, combinatorial proof of a Chernoff bound similar to the one by Impagliazzo and Kabanets (RANDOM, 2010).\n  In particular, we prove a randomized version of the hitting property of expander random walks and apply it to obtain a concentration bound for expander random walks which is essentially optimal for small deviations and a large number of steps. At the same time, we present a simpler proof that still yields a \"right\" bound settling a question asked by Impagliazzo and Kabanets.\n  Next, we obtain a simple upper tail bound for polynomials with input variable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2349","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"}