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Rate of convergence for polymers in a weak disorder

By Francis Comets and Quansheng Liu

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

Topics: regular martingale, rate of convergence, Directed polymers, random environment, weak disorder, central limit theorem for martingales, stable and mixing convergence, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Publisher: HAL CCSD
Year: 2016
OAI identifier: oai:HAL:hal-01316122v2
Provided by: Hal-Diderot

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