| Título: | Correlation Lengths for Random Polymer Models and for Some Renewal Sequences |
| Autores: | Toninelli, Fabio Lucio; ENS LYON |
| Fecha: | 2007-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Pinning and Wetting Models, Typical and Average Correlation Lengths, Critical Exponents, Renewal Theory, Exponential Convergence Rates 82B27, 82B44, 82B41, 60K05 |
| Descripción: | 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 $Z$. These models are known to undergo a delocalization-localization transition, and the free energy $F$ vanishes when the critical point is approached from the localized region. We prove that the quenched correlation length $\xi$, defined as the inverse of the rate of exponential decay of the two-point function, does not diverge faster than $1/F$. 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. |
| Idioma: | No aplica |
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