{"paper":{"title":"Cutoff for the transience and mixing time of a SSEP with traps and consequences on the FEP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Brune Massouli\\'e, Cl\\'ement Erignoux","submitted_at":"2024-03-29T06:50:32Z","abstract_excerpt":"We introduce a new particle system that we call the SSEP with traps, which is non reversible, attractive, and has a transient regime. We study its \\emph{transience time} $\\theta_K$, meaning the time after which the system is no longer in a transient state with high probability, on the ring with $K$ sites. We first show that $\\theta_K$ is of order $K^2 \\log K$ for a system of size $K$, and more precisely that it exhibits a cutoff at time $\\frac{1}{\\pi^2} K^2 \\log K$. We then show that its \\emph{mixing time} also undergoes cutoff at the same time.\n  We further define a new mapping between the SS"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.20010","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/2403.20010/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"}