@article{EJP2005,
author = {Kenneth Alexander and Nikolaos Zygouras},
title = {Subgaussian concentration and rates of convergence in directed polymers},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {directed polymers, concentration, modified Poincar\'e inequalities, coarse graining},
abstract = {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 $O( \sqrt{\frac{N}{\log N}}\log \log N)$},
pages = {no. 5, 1-28},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2005},
url = {http://ejp.ejpecp.org/article/view/2005}}