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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 ≥ 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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https://hal.archives-ouvertes.fr/hal-01316122
Contributor : Francis Comets <>
Submitted on : Tuesday, May 17, 2016 - 7:03:28 PM
Last modification on : Friday, March 27, 2020 - 3:56:34 AM
Document(s) archivé(s) le : Friday, August 19, 2016 - 5:27:42 PM

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  • HAL Id : hal-01316122, version 2
  • ARXIV : 1605.05108

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

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