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We prove a large deviations principle for the $q$-fold self-intersection local time $I_T=\\sum_{x\\in\\mathbb{Z}^d}l_T(x)^q$ in the critical case $q=\\frac{d}{d-2}$. When $q$ is integer, we obtain similar results for the intersection local times of $q$ independent simple random walks."},"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":"0812.1639","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-09T09:27:13Z","cross_cats_sorted":[],"title_canon_sha256":"374b60a9545d1d151d3b2e970eb939ba79d569f0eea89cef454cbbef179ed8f6","abstract_canon_sha256":"df3deaa21f4aa02a86ee9a7671dc170c2bc5746ba6b646dec4891e8367c1f6b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:59.700038Z","signature_b64":"pGE1nap2O5HaYR91oKNa5JIebC5rSZMpbsIEVt1BRIKTAKe92UAF9+yIU5XahfQL6b116zGdwF7X/kmkb2SkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ae953ae97273cab2f55dffad0045357ac28f8ad1e4d50f0d0aac9ece4d9c4e1","last_reissued_at":"2026-05-18T04:39:59.699431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:59.699431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large deviations for intersection local times in critical dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabienne Castell","submitted_at":"2008-12-09T09:27:13Z","abstract_excerpt":"Let $(X_t,t\\geq0)$ be a continuous time simple random walk on $\\mathbb{Z}^d$ ($d\\geq3$), and let $l_T(x)$ be the time spent by $(X_t,t\\geq0)$ on the site $x$ up to time $T$. We prove a large deviations principle for the $q$-fold self-intersection local time $I_T=\\sum_{x\\in\\mathbb{Z}^d}l_T(x)^q$ in the critical case $q=\\frac{d}{d-2}$. 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