{"paper":{"title":"Stability of Khintchine-type inequalities via log-monotonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"\\'Angel Ch\\'avez, Sam Sheng","submitted_at":"2026-06-17T17:34:52Z","abstract_excerpt":"We investigate Khintchine-type inequalities for the weighted sums $S=\\sum_ka_kX_k$ of independent copies of a symmetric random variable $X$. We show how log-monotonicity of the sequence $r_k(X)=k! \\mathbb{E}[X^{2k}]/(2k)!$ implies sharp comparisons between the $L_p$ and $L_2$ norms of $S$ for every even integer $p\\geq 2$, extending classic Khintchine-type inequalities and yielding new results in the log-convex setting. We also investigate the stability of our inequalities. Our first stability inequality sharpens the classic inequality by a deviation of the coefficient vector from the coordinat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19313","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.19313/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}