{"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 $\\mathbb{R}^d$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05597","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}