{"paper":{"title":"Scaling limit theorems for the $\\kappa$-transient random walk in random and non-random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hui Yang, Wenming Hong","submitted_at":"2014-12-14T08:34:44Z","abstract_excerpt":"Kesten et al.( 1975) proved the stable law for the transient RWRE (here we refer it as the $\\kappa$-transient RWRE). After that, some similar interesting properties have also been revealed for its continuous counterpart, the diffusion proces in a Brownian environment with drift $\\kappa$. In the present paper we will investigate the connections between these two kind of models, i.e., we will construct a sequence of the $\\kappa$-transient RWREs and prove it convergence to the diffusion proces in a Brownian environment with drift $\\kappa$ by proper scaling. To this end, we need a counterpart conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4326","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"}