Correlation lengths for random polymer models and for some renewal sequences
| dc.creator | Toninelli, F. L. | |
| dc.date | 2006-11-28 | |
| dc.date | 2006-12-08 | |
| dc.date.accessioned | 2026-07-07T08:08:27Z | |
| dc.date.available | 2026-07-07T08:08:27Z | |
| dc.description | We consider models of directed polymers interacting with a one-dimensional defect line on which random charges are placed. More abstractly, one starts from renewal sequence on $\Z$ and gives a random (site-dependent) reward or penalty to the occurrence of a renewal at any given point of $\mathbb Z$. These models are known to undergo a delocalization-localization transition, and the free energy $\tf$ vanishes when the critical point is approached from the localized region. We prove that the quenched correlation length $ξ$, defined as the inverse of the rate of exponential decay of the two-point function, does not diverge faster than $ 1/\tf$. We prove also an exponentially decaying upper bound for the disorder-averaged two-point function, with a good control of the sub-exponential prefactor. We discuss how, in the particular case where disorder is absent, this result can be seen as a refinement of the classical renewal theorem, for a specific class of renewal sequences. | |
| dc.description | 21 pages, 2 figures; v2: results generalized, few typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0611868 | |
| dc.identifier | http://arxiv.org/abs/math/0611868 | |
| dc.identifier | Electron. J. Probab. 12, 613-636 (2007) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131268 | |
| dc.subject | Probability | |
| dc.title | Correlation lengths for random polymer models and for some renewal sequences | |
| dc.type | text |