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In a recent paper, Claeys, Girotti and Stivigny have established first and second order asymptotics for large gap probabilities in these ensembles. These asymptotics take the form \\begin{equation*} \\mathbb{P}(\\mbox{gap on } [0,s]) = C \\exp \\left( -a s^{2\\rho} + b s^{\\rho} + c \\ln s \\right) (1 + o(1)) \\qquad \\mbox{as }s \\to + \\infty, \\end{equation*} where the constants $\\rho$, $a$, and $b$ ha"},"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":"1906.12130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-28T11:01:55Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4eca33cae6742305ac06417825284ddd4c0910128193472e54491bec5762889d","abstract_canon_sha256":"9a9dd129caf561509d785d9e75ed228f0cc8d2e3a18b7c6694353a020784c440"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:59.199648Z","signature_b64":"Z86qgdbC0LTcx4dhI4LUXnUCg9n842fOGzInu042+IYe7F0QIIvjyFswOgvpCxOIsQzk/CZqKQPBpjjdsWjeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9adb534cd3fcfe5065e0f6712930b640d17c20b7195c747b98883872fbfff6c","last_reissued_at":"2026-05-17T23:41:59.199281Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:59.199281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher order large gap asymptotics at the hard edge for Muttalib--Borodin ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Christophe Charlier, Jonatan Lenells, Julian Mauersberger","submitted_at":"2019-06-28T11:01:55Z","abstract_excerpt":"We consider the limiting process that arises at the hard edge of Muttalib--Borodin ensembles. 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