{"paper":{"title":"A Hoeffding inequality for Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Shravas Rao","submitted_at":"2018-06-29T16:22:24Z","abstract_excerpt":"We prove deviation bounds for the random variable $\\sum_{i=1}^{n} f_i(Y_i)$ in which $\\{Y_i\\}_{i=1}^{\\infty}$ is a Markov chain with stationary distribution and state space $[N]$, and $f_i: [N] \\rightarrow [-a_i, a_i]$. Our bound improves upon previously known bounds in that the dependence is on $\\sqrt{a_1^2+\\cdots+a_n^2}$ rather than $\\max_{i}\\{a_i\\}\\sqrt{n}.$ We also prove deviation bounds for certain types of sums of vector--valued random variables obtained from a Markov chain in a similar manner. One application includes bounding the expected value of the Schatten $\\infty$-norm of a random"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11519","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"}