{"paper":{"title":"Almost exponential decay for the exit probability from slabs of ballistic RWRE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alejandro F. Ramirez, Enrique Guerra","submitted_at":"2014-06-17T20:50:56Z","abstract_excerpt":"It is conjectured that in dimensions $d\\ge 2$ any random walk in an i.i.d. uniformly elliptic random environment (RWRE) which is directionally transient is ballistic. The ballisticity conditions for RWRE somehow interpolate between directional transience and ballisticity and have served to quantify the gap which would need to be proven in order to answer affirmatively this conjecture. Two important ballisticity conditions introduced by Sznitman \\cite{Sz02} in 2001 and 2002 are the so called conditions $(T')$ and $(T)$: given a slab of width $L$ orthogonal to $l$, condition $(T')$ in direction "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4537","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"}