{"paper":{"title":"Spectral Analysis of a Discrete Metastable System Driven by L\\'evy Flights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"math.PR","authors_text":"Ilya Pavlyukevich, Toralf Burghoff","submitted_at":"2015-01-14T07:35:57Z","abstract_excerpt":"In this paper we consider a finite state time discrete Markov chain that mimics the behaviour of solutions of the stochastic differential equation $dX=-U'(X)dt+\\epsilon dL$, where $U$ is a multi-well potential with $n\\geq 2$ local minima and L is a symmetric \\alpha-stable L\\'evy process (L\\'evy flights process). We investigate the spectrum of the generator of this Markov chain in the limit $\\epsilon\\to 0$ and localize the top n eigenvalues $\\lambda^\\epsilon_1,\\dots, \\lambda^\\epsilon_n$. These eigenvalues turn out to be of the same algebraic order $O(\\epsilon^\\alpha)$ and are well separated fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03264","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"}