### Subgaussian concentration and rates of convergence in directed polymers

**Kenneth S. Alexander**

*(University of Southern California)*

**Nikolaos Zygouras**

*(University of Warwick)*

#### 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 $O( \sqrt{\frac{N}{\log N}}\log \log N)$

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Pages: 1-28

Publication Date: January 11, 2013

DOI: 10.1214/EJP.v18-2005

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