{"paper":{"title":"Sparsity-adaptive concentration inequalities for random polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guozheng Dai, Ke Wang","submitted_at":"2026-06-23T03:10:49Z","abstract_excerpt":"We prove concentration inequalities for polynomials of independent, sparse $\\alpha$-sub-exponential random variables. Specifically, we consider $X_i=\\delta_i\\xi_i$, where the Bernoulli selectors $\\delta_i$ are independent with parameters $p_i$, and the variables $\\xi_i$ are independent \\(\\alpha\\)-sub-exponential random variables (not necessarily centered). For any polynomial $f:\\mathbb R^n\\to\\mathbb R $ of degree at most $D$ and any $0<\\alpha \\le 1 $, we establish an $L_r$-moment bound for \\(f(X)-\\mathbb E f(X)\\) in terms of partition norms of sparsity-weighted expected derivative tensors. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24090","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/2606.24090/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"}