Ballisticity conditions for random walk in random environment
| dc.creator | Drewitz, Alexander | |
| dc.creator | Ramírez, Alejandro F. | |
| dc.date | 2009-03-25 | |
| dc.date.accessioned | 2026-07-07T12:56:57Z | |
| dc.date.available | 2026-07-07T12:56:57Z | |
| dc.description | Consider a random walk in a uniformly elliptic i.i.d. random environment in dimensions $d\ge 2$. In 2002, Sznitman introduced for each $γ\in (0,1)$ the ballisticity conditions $(T)_γ$ and $(T'),$ the latter being defined as the fulfilment of $(T)_γ$ for all $γ\in (0,1).$ He proved that $(T')$ implies ballisticity and that for each $γ\in (0.5,1),$ $(T)_γ$ is equivalent to $(T')$. It is conjectured that this equivalence holds for all $γ\in (0,1).$ Here we prove that for $γ\in (γ_d,1),$ where $γ_d$ is a dimension dependent constant taking values in the interval $(0.366,0.388),$ $(T)_γ$ is equivalent to $(T').$ This is achieved by a detour along the effective criterion, the fulfilment of which we establish by a combination of techniques developed by Sznitman giving a control on the occurrence of atypical quenched exit distributions through boxes. | |
| dc.identifier | https://arxiv.org/abs/0903.4465 | |
| dc.identifier | http://arxiv.org/abs/0903.4465 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224761 | |
| dc.subject | Probability | |
| dc.subject | 60K37, 82D30 | |
| dc.title | Ballisticity conditions for random walk in random environment | |
| dc.type | text |