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We compute its rescaled asymptotic variance: \\[ \\lim_{t\\to\\infty} t^{-1/2} \\V J(t) = \\sqrt{2/\\pi} (1-\\rho)\\rho \\] Furthermore we show that $t^{-1/4}J(t)$ converges weakly to a centered normal random variable with this variance. From these results we compute the asymptotic variance of a tagged particle in the nearest neighbor case and show the corresponding central limit theorem, results previously proven by Arratia."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0103233","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2001-03-30T21:28:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f6d1aeacc989eec969a90125493672efcf4a20e1d68dc981ef94ecd9fb8f4b97","abstract_canon_sha256":"e0b15a0f1c0c4cd5bb4f3817904ca92be3434b43b6121ea0583b393a54a8af99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:43.219051Z","signature_b64":"1pH3bYy46VfxJYyPAMIbU9OEY+cUQurWWVrxRvn6PlcqJXupfhvTrz6FF6kAcHlCSA4igdP+g+yzXWsdN65XDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c10a130cce0f7233e5c658e00c8caf17fa2e46e60c0adca1fb31664109a3a13f","last_reissued_at":"2026-05-18T04:08:43.218621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:43.218621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flux fluctuations in the one dimensional nearest neighbors symmetric simple exclusion process","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"A. 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