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Pré-Publication, Document De Travail Année : 2016

Rate of convergence for polymers in a weak disorder

Résumé

We consider directed polymers in random environment on the lattice Z d at small inverse temperature and dimension d ≥ 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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Dates et versions

hal-01316122 , version 1 (14-05-2016)
hal-01316122 , version 2 (17-05-2016)

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Francis Comets, Quansheng Liu. Rate of convergence for polymers in a weak disorder. 2016. ⟨hal-01316122v2⟩
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