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We show that these two random variables can be mapped onto extreme value quantities associated to N independent random walkers. Using this mapping, we compute exactly their probability distributions P_N^d(S,t) and P_N^d(W,t) for any value of N in the limit of large time t, where the random walkers can be described by Brownian motions. In the large N limit one finds that S_N(t)/\\sqrt{t} \\propto 2 \\sqrt{\\log N} + \\widetilde{"},"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":"1302.2452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-02-11T11:26:41Z","cross_cats_sorted":["cond-mat.dis-nn","math.PR"],"title_canon_sha256":"89998fcf00d47aa643fd3edb8cd5488e193489cf6a70d436d880273885b339a5","abstract_canon_sha256":"bfe68045835a6bd58b083c5c37ce2e934e65da7f9b370e5164e2b8b2029b4d00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:42.430098Z","signature_b64":"QQNcc7Xkxy1NJmG1Cgc8b/ODGAWKgxkYx4ux5uys6WGuNCNgE5xJsJwLjIMxnOP0hQUTPk1vlfmM+SvK1V1gDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf1fe5b5e10f96367e2a49328829aef9f84e32a1c807590ec920e5d91d2fe932","last_reissued_at":"2026-05-18T03:18:42.429291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:42.429291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact distributions of the number of distinct and common sites visited by N independent random walkers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Anupam Kundu, Gregory Schehr, Satya N. 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