| Título: | Subgaussian concentration and rates of convergence in directed polymers |
| Autores: |
Alexander, Kenneth S.; University of Southern California Zygouras, Nikolaos; University of Warwick |
| Fecha: | 2013-01-04 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
directed polymers, concentration, modified Poincar\'e inequalities, coarse graining 82B44; 82D60; 60K35 |
| Descripción: | We consider directed random polymers in $(d+1)$ dimensions with nearly gamma i.i.d. disorder. We study the partition function $Z_{N,\omega}$ and establish exponential concentration of $\log Z_{N,\omega}$ about its mean on the subgaussian scale $\sqrt{N/\log N}$ . This is used to show that $\mathbb{E}[ \log Z_{N,\omega}]$ differs from $N$ times the free energy by an amount which is also subgaussian (i.e. $o(\sqrt{N})$), specifically $O( \sqrt{\frac{N}{\log N}}\log \log N)$ |
| Idioma: | Inglés |
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