{"paper":{"title":"Atypical behaviors of a tagged particle in asymmetric simple exclusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"S.R.S. Varadhan, Sunder Sethuraman","submitted_at":"2023-11-13T23:30:28Z","abstract_excerpt":"Consider the asymmetric nearest-neighbor exclusion process (ASEP) on ${\\mathbb Z}$ with single particle drift $\\gamma>0$, starting from a Bernoulli product invariant measure $\\nu_\\rho$ with density $\\rho$. It is known that the position $X_{N}$ of a tagged particle, say initially at the origin, at time $N$ satisfies an a.s. law of large numbers $\\frac{1}{N}X_N \\rightarrow \\gamma(1-\\rho)$ as $N\\uparrow\\infty$.\n  In this context, we study the `typical' behavior of the tagged particle and `bulk' density evolution subject to `atypical' events $\\{X_N\\geq AN\\}$ or $\\{X_N\\leq AN\\}$ for $A\\neq \\gamma(1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.07800","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/2311.07800/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"}