Rate of convergence for polymers in a weak disorder

Francis Comets; Quansheng Liu

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arXiv · 1605.05108

Rate of convergence for polymers in a weak disorder

Francis Comets·Quansheng Liu

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Abstract

We consider directed polymers in random environment on the lattice Z d at small inverse temperature and dimension d $\ge$ 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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Francis Comets, Quansheng Liu. 2016-05-18. Rate of convergence for polymers in a weak disorder. https://arxiv.org/abs/1605.05108

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