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It can be written as a Fredholm determinant with discontinuities, or equivalently as the convergent series \\begin{equation*} \\sum_{k_{1},...,k_{m} \\geq 0} \\mathbb{P}\\Bigg(\\bigcap_{j=1}^{m} \\#\\{\\mbox{points in j-th interval}\\}=k_{j}\\Bigg)\\prod_{j=1}^{m} s_{j}^{k_{j}}, \\end{equation*} where $s_{1},\\ldots,s_{m} \\in [0,1]$. In particular, we can deduce from it joint probabilities of the counting function of the process. In this work, we obtain large gap asymptotics for the generating function, which are asy"},"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":"1906.11079","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-25T07:18:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"147c94ea566dbac3c7a8ed577cf68d278ebf3a1218eff5df57e0f6b0d1aa333e","abstract_canon_sha256":"e01881b2d2211d9ce368945ab14b0c8b48db8903833ceaeb8279397e14ce9971"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:38:11.964686Z","signature_b64":"0PQPAljL9RDDscfKUkb24LMKNxUjqseOi1fPCGxiRSjjHHACPXpgisCxEK4uEH9eRFBhEZgcdsKd8oVTVfF3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f5b57ed95caf8b66fbfce479b8db643d13248427010051155e04d18d1012781","last_reissued_at":"2026-07-05T02:38:11.964186Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:38:11.964186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large gap asymptotics for the generating function of the sine point process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Christophe Charlier","submitted_at":"2019-06-25T07:18:02Z","abstract_excerpt":"We consider the generating function of the sine point process on $m$ consecutive intervals. 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