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Subgaussian concentration and rates of convergence in directed polymers
2013
Electronic Journal of Probability
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We consider directed random polymers in (d+1) dimensions with nearly gamma i.i.d. disorder. We study the partition function Z_N,ω and establish exponential concentration of Z_N,ω about its mean on the subgaussian scale √(N/ N) . This is used to show that E[ Z_N,ω] differs from N times the free energy by an amount which is also subgaussian (i.e. o(√(N))), specifically O(√(N/ N) N).
doi:10.1214/ejp.v18-2005
fatcat:sw2n4ulpvjeczngvlcfzdzucmm