{"paper":{"title":"Quenched exit estimates and ballisticity conditions for higher-dimensional random walk in random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alejandro F. Ram\\'irez, Alexander Drewitz","submitted_at":"2010-05-03T19:33:14Z","abstract_excerpt":"Consider a random walk in an i.i.d. uniformly elliptic environment in dimensions larger than one. In 2002, Sznitman introduced for each $\\gamma\\in(0,1)$ the ballisticity condition $(T)_{\\gamma}$ and the condition $(T')$ defined as the fulfillment of $(T)_{\\gamma}$ for each $\\gamma\\in(0,1)$. Sznitman proved that $(T')$ implies a ballistic law of large numbers. Furthermore, he showed that for all $\\gamma\\in (0.5,1)$, $(T)_{\\gamma}$ is equivalent to $(T')$. Recently, Berger has proved that in dimensions larger than three, for each $\\gamma\\in (0,1)$, condition $(T)_{\\gamma}$ implies a ballistic la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0376","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"}