{"paper":{"title":"Random walk in the low disorder ballistic regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alejandro F. Ramirez","submitted_at":"2016-02-19T20:57:49Z","abstract_excerpt":"We consider a random walk in $\\mathbb Z^d$ which jumps from a site $x$ to a nearest neighboring site $x+e$ (where $e\\in V:=\\{x\\in\\mathbb Z^d: |x|_1=1\\}$) with probability $p_0(e)+\\epsilon\\xi(x,e)$. Here $\\sum_e p_0(e)=1$, $p_0(e)> 0$, $\\epsilon$ is a small parameter while $\\{\\{\\xi (x,e):e\\in V\\}: x\\in\\mathbb Z^d\\}$ are i.i.d. random variables with an absolute value bounded by $1$. We review recent progress in the non-vanishing velocity case, giving an asymptotic expansion in $\\epsilon$ of the invariant measure of the environmental process, and bounds for the velocity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06292","kind":"arxiv","version":2},"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"}