{"paper":{"title":"Total Variation Discrepancy of Deterministic Random Walks for Ergodic Markov Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Masafumi Yamashita, Shuji Kijima, Takeharu Shiraga, Yukiko Yamauchi","submitted_at":"2015-08-14T10:15:53Z","abstract_excerpt":"Motivated by a derandomization of Markov chain Monte Carlo (MCMC), this paper investigates deterministic random walks, which is a deterministic process analogous to a random walk. While there are several progresses on the analysis of the vertex-wise discrepancy (i.e., $L_\\infty$ discrepancy), little is known about the {\\em total variation discrepancy} (i.e., $L_1$ discrepancy), which plays a significant role in the analysis of an FPRAS based on MCMC. This paper investigates upper bounds of the $L_1$ discrepancy between the expected number of tokens in a Markov chain and the number of tokens in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03458","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":""},"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"}