## Actes des rencontres du CIRM

Table des matières de ce fascicule | Article précédent
Nikolaos Zygouras
Semidirected random polymers: Strong disorder and localization
Actes des rencontres du CIRM, 2 no. 1: Déviations pour les temps locaux d’auto-intersections (2010), p. 47-48, doi: 10.5802/acirm.25
Article PDF

Résumé - Abstract

Semi-directed, random polymers can be modeled by a simple random walk on $Z^d$ in a random potential -$(\lambda +\beta \omega (x))_{x\in Z^d}$, where $\lambda >0$, $\beta >0$ and $\left(\,\omega (x)\,\right)_{x\in Z^d}$ is a collection of i.i.d., nonnegative random variables. We identify situations where the annealed and quenched costs, that the polymer pays to perform long crossings are different. In these situations we show that the polymer exhibits localization.

Bibliographie

[1] Giacomin, Giacomin; Lacoin, Hubert; Toninelli, Fabio L.; Marginal relevance of disorder for pinning models. Comm. Pure Appl. Math. 63 (2010) 233-265.  MR 2588461 |  Zbl 1189.60173
[2] Lacoin, Hubert; New bounds for the free energy of directed polymer in dimension 1+1 and 1+2. Comm. Math. Phys. 294 (2010) 471-503.  MR 2579463
[3] Ioffe, Dmitry; Velenik, Yvan; Crossing random walks and stretched polymers at weak disorder. arXiv:1002.4289
arXiv
[4] Vargas, Vincent; Strong localization and macroscopic atoms for directed polymers Prob. Theory Rel. Fields Volume 138, Numbers 3-4 (2007)  MR 2299713 |  Zbl 1113.60097
[5] Zygouras, N.; Strong disorder in semidirected random polymers. arxiv.org/abs/1009.2693
arXiv
Copyright Cellule MathDoc 2013 | Crédit | Plan du site