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2013 Subgaussian concentration and rates of convergence in directed polymers
Kenneth Alexander, Nikolaos Zygouras
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Electron. J. Probab. 18: 1-28 (2013). DOI: 10.1214/EJP.v18-2005


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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Kenneth Alexander. Nikolaos Zygouras. "Subgaussian concentration and rates of convergence in directed polymers." Electron. J. Probab. 18 1 - 28, 2013.


Accepted: 11 January 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1281.82036
MathSciNet: MR3024099
Digital Object Identifier: 10.1214/EJP.v18-2005

Primary: 82B44
Secondary: 60K35 , 82D60

Keywords: coarse graining , Concentration , Directed polymers , modified Poincar\'e inequalities

Vol.18 • 2013
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