{"paper":{"title":"Lyapunov exponents of random walks in small random potential: the upper bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Christophe Mourrat, Thomas Mountford","submitted_at":"2014-04-28T16:45:41Z","abstract_excerpt":"We consider the simple random walk on $\\mathbb{Z}^d$ evolving in a random i.i.d. potential taking values in $[0,+\\infty)$. The potential is not assumed integrable, and can be rescaled by a multiplicative factor $\\lambda > 0$. Completing the work started in a companion paper, we give the asymptotic behaviour of the Lyapunov exponents for $d \\ge 3$, both annealed and quenched, as the scale parameter $\\lambda$ tends to zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7051","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"}