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Differing Averaged and Quenched Large Deviations for Random Walks in Random Environments in Dimensions Two and Three
| Content Provider | Paperity |
|---|---|
| Author | Zeitouni, Ofer Yilmaz, Atilla |
| Abstract | We consider the quenched and the averaged (or annealed) large deviation rate functions I q and I a for space-time and (the usual) space-only RWRE on \({\mathbb{Z}^d}\) . By Jensen’s inequality, I a ≤ I q . In the space-time case, when d ≥ 3 + 1, I q and I a are known to be equal on an open set containing the typical velocity ξ o . When d = 1 + 1, we prove that I q and I a are equal only at ξ o . Similarly, when d = 2 + 1, we show that I a < I q on a punctured neighborhood of ξ o . In the space-only case, we provide a class of non-nestling walks on \({\mathbb{Z}^d}\) with d = 2 or 3, and prove that I q and I a are not identically equal on any open set containing ξ o whenever the walk is in that class. This is very different from the known results for non-nestling walks on \({\mathbb{Z}^d}\) with d ≥ 4. |
| Starting Page | 243 |
| Ending Page | 271 |
| File Format | HTM / HTML |
| ISSN | 00103616 |
| DOI | 10.1007/s00220-010-1119-3 |
| Issue Number | 1 |
| Journal | Communications in Mathematical Physics |
| Volume Number | 300 |
| e-ISSN | 14320916 |
| Language | English |
| Publisher | Springer Berlin Heidelberg |
| Publisher Date | 2010-11-01 |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistical and Nonlinear Physics Mathematical Physics |
