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We show that $\\E[\\vol(\\cup_{s \\leq t}(\\xi(s) + D_s))] \\geq \\E[\\vol(\\cup_{s \\leq t}(\\xi(s) + B_s))]$, for all $t$. In particular, this implies that the expected volume of the Wiener sausage increases when a drift is added to the Brownian motion."},"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":"1103.6059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-30T22:46:33Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"13cc4dea2fc828844dedb24766712c36f27d1f2f9f204311c31946193e0ad33c","abstract_canon_sha256":"40e387b320730cbdcf77559dc164e6075ed87fbb7058d6523c54430a6163ca16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:25.282127Z","signature_b64":"fuzaF+wG0q/7uXkBdVzSaXe26TzzwkUw3ejyZ83ohnc/HQwaVEisBOWaa/y7q1YWl7jo/hEZ3GZOkXiPiIbDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"027bc125409b1106a18afad320f56f1b89842614e39354bc353043aa9b98f6b7","last_reissued_at":"2026-05-18T04:25:25.281399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:25.281399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An isoperimetric inequality for the Wiener sausage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Perla Sousi, Yuval Peres","submitted_at":"2011-03-30T22:46:33Z","abstract_excerpt":"Let $(\\xi(s))_{s\\geq 0}$ be a standard Brownian motion in $d\\geq 1$ dimensions and let $(D_s)_{s \\geq 0}$ be a collection of open sets in $\\R^d$. For each $s$, let $B_s$ be a ball centered at 0 with $\\vol(B_s) = \\vol(D_s)$. We show that $\\E[\\vol(\\cup_{s \\leq t}(\\xi(s) + D_s))] \\geq \\E[\\vol(\\cup_{s \\leq t}(\\xi(s) + B_s))]$, for all $t$. In particular, this implies that the expected volume of the Wiener sausage increases when a drift is added to the Brownian motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6059","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1103.6059","created_at":"2026-05-18T04:25:25.281506+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.6059v1","created_at":"2026-05-18T04:25:25.281506+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.6059","created_at":"2026-05-18T04:25:25.281506+00:00"},{"alias_kind":"pith_short_12","alias_value":"AJ54CJKATMIQ","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"AJ54CJKATMIQNIMK","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"AJ54CJKA","created_at":"2026-05-18T12:26:24.575870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AJ54CJKATMIQNIMK7LJSB5LPDO","json":"https://pith.science/pith/AJ54CJKATMIQNIMK7LJSB5LPDO.json","graph_json":"https://pith.science/api/pith-number/AJ54CJKATMIQNIMK7LJSB5LPDO/graph.json","events_json":"https://pith.science/api/pith-number/AJ54CJKATMIQNIMK7LJSB5LPDO/events.json","paper":"https://pith.science/paper/AJ54CJKA"},"agent_actions":{"view_html":"https://pith.science/pith/AJ54CJKATMIQNIMK7LJSB5LPDO","download_json":"https://pith.science/pith/AJ54CJKATMIQNIMK7LJSB5LPDO.json","view_paper":"https://pith.science/paper/AJ54CJKA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.6059&json=true","fetch_graph":"https://pith.science/api/pith-number/AJ54CJKATMIQNIMK7LJSB5LPDO/graph.json","fetch_events":"https://pith.science/api/pith-number/AJ54CJKATMIQNIMK7LJSB5LPDO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AJ54CJKATMIQNIMK7LJSB5LPDO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AJ54CJKATMIQNIMK7LJSB5LPDO/action/storage_attestation","attest_author":"https://pith.science/pith/AJ54CJKATMIQNIMK7LJSB5LPDO/action/author_attestation","sign_citation":"https://pith.science/pith/AJ54CJKATMIQNIMK7LJSB5LPDO/action/citation_signature","submit_replication":"https://pith.science/pith/AJ54CJKATMIQNIMK7LJSB5LPDO/action/replication_record"}},"created_at":"2026-05-18T04:25:25.281506+00:00","updated_at":"2026-05-18T04:25:25.281506+00:00"}