Subgaussian concentration and rates of convergence in directed polymers
نویسندگان
چکیده
We consider directed random polymers in (d+1) dimensions with nearly gamma i.i.d. disorder. We study the partition function ZN,ω and establish exponential concentration of logZN,ω about its mean on the subgaussian scale √ N/ logN . This is used to show that E[logZN,ω] differs from N times the free energy by an amount which is also subgaussian (i.e. o( √ N)), specifically O( √ N logN log logN).
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تاریخ انتشار 2012