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Rate of convergence for polymers in a weak disorder

Abstract : We consider directed polymers in random environment on the lattice $Z^d$ at small inverse temperature and dimension $d \geq 3$. Then, the normalized partition function $W_n$ is a regular martingale with limit W. We prove that $n^{(d−2)/4} (W_n−W)/W_n $ converges in distribution to a Gaussian law. Both the polynomial rate of convergence and the scaling with the martingale $W_n$ are different from those for polymers on trees.
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Submitted on : Friday, February 9, 2018 - 9:23:20 PM
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Francis Comets, Quansheng Liu. Rate of convergence for polymers in a weak disorder. Journal of Mathematical Analysis and Applications, Elsevier, 2017, 455 (1), pp.312 - 335. ⟨10.1016/j.jmaa.2017.05.043⟩. ⟨hal-01705859⟩

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