{"paper":{"title":"Asymptotic expansion of the invariant measure for ballistic random walk in the low disorder regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alejandro F. Ramirez, David Campos","submitted_at":"2015-11-10T00:33:05Z","abstract_excerpt":"We consider a random walk in random environment in the low disorder regime on $\\mathbb Z^d$. That is, the probability that the random walk jumps from a site $x$ to a nearest neighboring site $x+e$ is given by $p(e)+\\epsilon \\xi(x,e)$, where $p(e)$ is deterministic, $\\{\\{\\xi(x,e):|e|_1=1\\}:x\\in\\mathbb Z^d\\}$ are i.i.d. and $\\epsilon>0$ is a parameter which is eventually chosen small enough. We establish an asymptotic expansion in $\\epsilon$ for the invariant measure of the environmental process whenever a ballisticity condition is satisfied. As an application of our expansion, we derive a numer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02945","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"}