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Becker and K\\\"onig have recently proved a large deviations principle for $I_t$ for all $(p,d)\\in\\mathbb{R}^d\\times\\mathbb{Z}^d$ such that $p(d-2)<2$. We extend these results to a broader scale of deviations and to the whole subcritical domain $p(d-2)<d$. Moreover we unify the proofs of the large deviations principle using a method introduced by Castell for the critical c"},"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":"1011.6486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-30T09:02:04Z","cross_cats_sorted":[],"title_canon_sha256":"24723408c9976aa676ba03a4befdbde2cf5628380bd9c969e30ee934a4f9cb41","abstract_canon_sha256":"0ae59f84f38301ccdd0004ce4ef5369fab2c52f8664835f9196165fa06a8ee83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:26.814488Z","signature_b64":"M9hr99q8W8XJhsIHHSNWweMo6Y7GhXeex98lVIe0P9tBu4dw5TLqjcBkl3n5V7j6+M9YhqhWvFRJ12fm3WWvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f52b8ff19dd4caef6d2081d61a7f803e007a91c37ad2235ae4d154e386fad762","last_reissued_at":"2026-05-18T04:34:26.813853Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:26.813853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large deviations for self-intersection local times in subcritical dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cl\\'ement Laurent","submitted_at":"2010-11-30T09:02:04Z","abstract_excerpt":"Let $(X_t,t\\geq 0)$ be a random walk on $\\mathbb{Z}^d$. Let $ l_t(x)= \\int_0^t \\delta_x(X_s)ds$ be the local time at site $x$ and $ I_t= \\sum\\limits_{x\\in\\mathbb{Z}^d} l_t(x)^p $ the p-fold self-intersection local time (SILT). Becker and K\\\"onig have recently proved a large deviations principle for $I_t$ for all $(p,d)\\in\\mathbb{R}^d\\times\\mathbb{Z}^d$ such that $p(d-2)<2$. We extend these results to a broader scale of deviations and to the whole subcritical domain $p(d-2)<d$. 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