{"paper":{"title":"Establishing an $\\Omega(\\sqrt{d})$ complexity lower bound for PDMP samplers and how to break it: a sub-$\\sqrt{d}$ algorithm for Gaussian-tailed targets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR","stat.ME"],"primary_cat":"stat.CO","authors_text":"Augustin Chevallier","submitted_at":"2026-06-18T08:04:12Z","abstract_excerpt":"Despite the theoretical appeal of their non-reversibility, to date, no Piecewise Deterministic Markov Process (PDMP) samplers have been developed that scale better than $\\mathcal{O}(\\sqrt{d})$ in computational complexity with respect to the target dimension $d$. We prove that this is a fundamental limitation by establishing an $\\Omega(\\sqrt{d})$ lower bound on the algorithmic complexity of PDMP samplers in a standard setup. By relaxing the assumption that the target density must remain invariant at all continuous times, we then demonstrate how to bypass this barrier. Specifically, we introduce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19909","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/2606.19909/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"}