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Such a function is a probabilistic solution to the parabolic eq. involving the nonlocal Schr\\\"odinger operator based on the generator of $(X_t)_{t \\geq 0}$ with potential $V^{\\omega}$. For a large class of processes and potentials, we determine rate functions $\\eta(t)$ and positive constants $C_1, C_2$ such that \\[-C_1"},"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":"1601.05597","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-21T12:00:11Z","cross_cats_sorted":["math.FA","math.SP"],"title_canon_sha256":"4779b3033358776603a38d900118ab766d40576a9e9e53e8c968286a82b6740a","abstract_canon_sha256":"3d2ca89e41b8716385f2b263ba4d5fe21d93e115fb40ae8a27d8125910969bfc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:13.409887Z","signature_b64":"uS+miszaKZCKvwBgxor//N29b9nQQ0n8UWD0QtC6mFF/WX/RSNfONnTYMdlrPeUgClFin6Pv1Or6j+uDwR6PAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04baf873c1642bce9c6b98df02df4ebf9b15927641a6a8820084018ecd223158","last_reissued_at":"2026-05-18T01:22:13.409273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:13.409273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The quenched asymptotics for nonlocal Schr\\\"odinger operators with Poissonian potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.SP"],"primary_cat":"math.PR","authors_text":"Kamil Kaleta, Katarzyna Pietruska-Pa{\\l}uba","submitted_at":"2016-01-21T12:00:11Z","abstract_excerpt":"We study the quenched long time behaviour of the survival probability up to time $t$, $\\mathbf{E}_x\\big[e^{-\\int_0^t V^{\\omega}(X_s){\\rm d}s}\\big],$ of a symmetric L\\'evy process with jumps, under a sufficiently regular Poissonian random potential $V^{\\omega}$ on $\\mathbb{R}^d$. 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