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We show the exact asymptotics of $P_x(\\tau>t) = C h(x)t^{-\\alpha}e^{-\\gamma t}(1 + o(1))$ as $t\\to\\infty$ and identify $C,h(x),\\alpha,\\gamma$ in terms of the drifts."},"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":"0704.0215","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-04-02T15:27:17Z","cross_cats_sorted":[],"title_canon_sha256":"fbe8193f0059758d37b9ba0f8e3be03955ac075a2718f438394c093a59a1c75d","abstract_canon_sha256":"7eb6280b237a0ed07ce2b14a966008fcd93bd4f179bdf16b54b193f3a4d8f68a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:10.908729Z","signature_b64":"IsVmN3msh/FEIm/u9DQE2zuXcro1iY/m7LW3hwPJOibrFlKhU5hBf0oK+d1jGYAekPNf+B2Mx+1l5JZgyqKSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c981f08e8ad2e51bc6776d2b2c89fe66bb7ba6e816f0f0573679f301c97ec08d","last_reissued_at":"2026-05-18T04:16:10.908096Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:10.908096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Tomasz Rolski, Zbigniew Pucha{\\l}a","submitted_at":"2007-04-02T15:27:17Z","abstract_excerpt":"In this note we consider the time of the collision $\\tau$ for $n$ independent Brownian motions $X^1_t,...,X_t^n$ with drifts $a_1,...,a_n$, each starting from $x=(x_1,...,x_n)$, where $x_1<...<x_n$. 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